arXiv subjects

Alex Cameron

Publications and source records attributed to Alex Cameron.

At least 19 recordsLinked to original sources

arXiv2024

JADES: The star-formation and chemical enrichment history of a luminous galaxy at z~9.43 probed by ultra-deep JWST/NIRSpec spectroscopy

We analyse ultra-deep JWST observations of the galaxy JADES-GS-z9-0 at z = 9.4327, and derive detailed stellar and interstellar medium (ISM) properties of this luminous (MUV=-20.43) high-redshift system. Complementary information from NIRCam imaging and NIRSpec (both low- and medium-resolution) spectroscopy reveal a compact system (Re ~110 pc) characterised by a steeply rising star formation history, which is reflected in the inferred young stellar age (t ~ 3 Myr, light-weighted), high star-formation rate surface density ({\Sigma}SFR ~ 72 M yr-1 kpc-2), high ionisation parameter (log(U) ~ -1.5), low metallicity (12+log(O/H) ~ 7.5), and low carbon-over-oxygen abundance ([C/O] = -0.64). Leveraging the detection of N iii]1750 we derive nitrogen-over-oxygen abundance ([N/O] ~ 0) higher than the plateau followed by low-redshift galaxies of similar metallicity, possibly revealing the imprint from (very) massive stars on the ISM enrichment and favouring a top-heavy Initial Mass Function (IMF) scenario. Massive stars powering a hard radiation field are also required to explain the rest-frame UV line ratios, though the presence of the high-excitation [Ne v]{\lambda}3426 emission line possibly hints at additional ionization from an AGN. We also report the tentative detection of Ly{\alpha} emission in the G140M spectrum, shifted by ~450 km/s redward of the systemic redshift. Combined with a modelling of the Ly{\alpha} spectral break, we rule out the presence of very high column densities of neutral gas pertaining to local absorbers, as well as any extended surrounding ionised bubble, suggesting that JADES-GS-z9-0 has not yet significantly contributed to cosmic Reionization.

astro-ph.GA↗

arXiv2023

JADES: Insights on the low-mass end of the mass--metallicity--star-formation rate relation at $3 < z < 10$ from deep JWST/NIRSpec spectroscopy

We analyse the gas-phase metallicity properties of a sample of low stellar mass (log M*/M_sun <= 9) galaxies at 3 < z < 10, observed with JWST/NIRSpec as part of the JADES programme in its deep GOODS-S tier. By combining this sample with more massive galaxies at similar redshifts from other programmes, we study the scaling relations between stellar mass, oxygen abundance (O/H), and star-formation rate (SFR) for 146 galaxies, spanning across three orders of magnitude in stellar mass and out to the epoch of early galaxy assembly. We find evidence for a shallower slope at the low-mass-end of the mass-metallicity relation (MZR), with 12 + log(O/H) = (7.72+-0.02) + (0.17+-0.03) log(M* / 10^8 M_sun), in good agreement with the MZR probed by local analogues of high-redshift systems like 'Green Pea' and 'Blueberry' galaxies. The inferred slope is well matched by models including 'momentum-driven' SNe winds, suggesting that feedback mechanisms in dwarf galaxies (and at high-z) might be different from those in place at higher masses. The evolution in the normalisation is observed to be relatively mild compared to previous determinations of the MZR at z~3 (~ 0.1 - 0.2 dex across the explored mass regime). We observe a deviation from the local fundamental metallicity relation (FMR) for our sample at high redshift, especially at z > 6, with galaxies significantly less enriched (with a median offset in log(O/H) of ~ 0.5 dex, significant at ~ 5 sigma) than predicted given their M* and SFR. These observations are consistent with an enhanced stochasticity in the star-formation history, and/or with an increased efficiency in metal removals by outflows, prompting us to reconsider the nature of the relationship between M*, O/H, and SFR in the early Universe.

astro-ph.GA↗

arXiv2022

Spectroscopic confirmation of four metal-poor galaxies at z=10.3-13.2

Finding and characterising the first galaxies that illuminated the early Universe at cosmic dawn is pivotal to understand the physical conditions and the processes that led to the formation of the first stars. In the first few months of operations, imaging from the James Webb Space Telescope (JWST) have been used to identify tens of candidates of galaxies at redshift (z) greater than 10, less than 450 million years after the Big Bang. However, none of these candidates has yet been confirmed spectroscopically, leaving open the possibility that they are actually low-redshift interlopers. Here we present spectroscopic confirmation and analysis of four galaxies unambiguously detected at redshift 10.3<z<13.2, previously selected from NIRCam imaging. The spectra reveal that these primeval galaxies are extremely metal poor, have masses between 10^7 and a few times 10^8 solar masses, and young ages. The damping wings that shape the continuum close to the Lyman edge are consistent with a fully neutral intergalactic medium at this epoch. These findings demonstrate the rapid emergence of the first generations of galaxies at cosmic dawn.

astro-ph.GA↗

arXiv2022

The Science Performance of JWST as Characterized in Commissioning

This paper characterizes the actual science performance of the James Webb Space Telescope (JWST), as determined from the six month commissioning period. We summarize the performance of the spacecraft, telescope, science instruments, and ground system, with an emphasis on differences from pre-launch expectations. Commissioning has made clear that JWST is fully capable of achieving the discoveries for which it was built. Moreover, almost across the board, the science performance of JWST is better than expected; in most cases, JWST will go deeper faster than expected. The telescope and instrument suite have demonstrated the sensitivity, stability, image quality, and spectral range that are necessary to transform our understanding of the cosmos through observations spanning from near-earth asteroids to the most distant galaxies.

astro-ph.IM↗

arXiv2022

Seaweed algebras

The index of a Lie algebra is an important algebraic invariant, but it is notoriously difficult to compute. However, for the suggestively-named seaweed algebras, the computation of the index can be reduced to a combinatorial formula based on the connected components of a "meander": a planar graph associated with the algebra. Our index analysis on seaweed algebras requires only basic linear and abstract algebra. Indeed, the main goal of this survey-type article is to introduce a broader audience to seaweed algebras with minimal appeal to specialized language and notation from Lie theory. This said, we present several results that do not appear elsewhere and do appeal to more advanced language in the Introduction to provide added context.

math.RA↗

arXiv2021

The unbroken spectra of Frobenius seaweeds

We show that if $\mathfrak{g}$ is a Frobenius seaweed, then the spectrum of the adjoint of a principal element consists of an unbroken set of integers whose multiplicities have a symmetric distribution. Our methods are combinatorial.

math.CO↗

arXiv2021

The breadth of Lie poset algebras

The breadth of a Lie algebra $L$ is defined to be the maximal dimension of the image of $ad_x=[x,-]:L\to L$, for $x\in L$. Here, we initiate an investigation into the breadth of three families of Lie algebras defined by posets and provide combinatorial breadth formulas for members of each family.

math.RA↗

arXiv2020

New Upper Bounds for the Erd\H{o}s-Gy\'arf\'as Problem on Generalized Ramsey Numbers

A $(p,q)$-coloring of a graph $G$ is an edge-coloring of $G$ which assigns at least $q$ colors to each $p$-clique. The problem of determining the minimum number of colors, $f(n,p,q)$, needed to give a $(p,q)$-coloring of the complete graph $K_n$ is a natural generalization of the well-known problem of identifying the diagonal Ramsey numbers $r_k(p)$. The best-known general upper bound on $f(n,p,q)$ was given by Erd\H{o}s and Gy\'arf\'as in 1997 using a probabilistic argument. Since then, improved bounds in the cases where $p=q$ have been obtained only for $p\in\{4,5\}$, each of which was proved by giving a deterministic construction which combined a $(p,p-1)$-coloring using few colors with an algebraic coloring. In this paper, we provide a framework for proving new upper bounds on $f(n,p,p)$ in the style of these earlier constructions. We characterize all colorings of $p$-cliques with $p-1$ colors which can appear in our modified version of the $(p,p-1)$-coloring of Conlon, Fox, Lee, and Sudakov. This allows us to greatly reduce the amount of case-checking required in identifying $(p,p)$-colorings, which would otherwise make this problem intractable for large values of $p$. In addition, we generalize our algebraic coloring from the $p=5$ setting and use this to give improved upper bounds on $f(n,6,6)$ and $f(n,8,8)$.

math.CO↗

arXiv2020

A lower bound on the saturation number, and graphs for which it is sharp

Let $H$ be a fixed graph. We say that a graph $G$ is $H$-saturated if it has no subgraph isomorphic to $H$, but the addition of any edge to $G$ results in an $H$-subgraph. The saturation number $\mathrm{sat}(H,n)$ is the minimum number of edges in an $H$-saturated graph on $n$ vertices. K\'aszonyi and Tuza, in 1986, gave a general upper bound on the saturation number of a graph $H$, but a nontrivial lower bound has remained elusive. In this paper we give a general lower bound on $\mathrm{sat}(H,n)$ and prove that it is asymptotically sharp (up to an additive constant) on a large class of graphs. This class includes all threshold graphs and many graphs for which the saturation number was previously determined exactly. Our work thus gives an asymptotic common generalization of several earlier results. The class also includes disjoint unions of cliques, allowing us to address an open problem of Faudree, Ferrara, Gould, and Jacobson.

math.CO↗

arXiv2019

Distance domatic numbers for grid graphs

We say that a vertex-coloring of a graph is a proper k-distance domatic coloring if for each color, every vertex is within distance k from a vertex receiving that color. The maximum number of colors for which such a coloring exists is called the k-distance domatic number of the graph. The problem of determining the k-distance domatic number is motivated by questions about multi-agent networks including arrangements of sensors and robotics. Here, we find the exact k-distance domatic numbers for all grid graphs formed from the Cartesian product of two sufficiently long paths.

math.CO↗

arXiv2019

Prospects for extending the Mass-Metallicity Relation to low mass at high redshift: a case study at z~1

We report J-band MOSFIRE spectroscopy of a low-mass (log$(M_*/M_\odot)=8.62^{+0.10}_{-0.06}$) star-forming galaxy at $z=0.997$ showing the detection of [NII] and [SII] alongside a strong H$\alpha$ line. We derive a gas-phase metallicity of log$(\text{O}/\text{H})=7.99^{+0.13}_{-0.23}$, placing this object in a region of $M_* - Z$ space that is sparsely populated at this redshift. Furthermore, many existing metallicity measurements in this $M_* - z$ regime are derived from only [NII]/H$\alpha$ (N2), a diagnostic widely used in high-redshift metallicity studies despite the known strong degeneracy with the ionization parameter and resulting large systematic uncertainty. We demonstrate that even in a regime where [NII] and [SII] are at the detection limit and the measurement uncertainty associated with the [NII]/[SII] ratio is high (S/N~3), the more sophisticated Dopita et al. diagnostic provides an improved constraint compared to N2 by reducing the systematic uncertainty due to the ionization parameter. This approach does not, however, dispel uncertainty associated with stochastic or systematic variations in the nitrogen-to-oxygen abundance ratio. While this approach improves upon N2, future progress in extending metallicity studies into this low-mass regime will require larger samples to allow for stochastic variations, as well as careful consideration of the global trends among dwarf galaxies in all physical parameters, not just metallicity.

astro-ph.GA↗

arXiv2019

Combinatorial index formulas for Lie algebras of seaweed type

Analogous to the types A, B, and C cases, we address the computation of the index of seaweed subalgebras in the type-D case. Formulas for the algebra's index can be computed by counting the connected components of its associated meander. We focus on a set of distinguished vertices of the meander, called the tail of the meander, and using the tail, we provide comprehensive combinatorial formulas for the index of a seaweed in all the classical types. Using these formulas, we provide all general closed-form index formulas where the index is given by a polynomial greatest common divisor formula in the sizes of the parts that define the seaweed.

math.RA↗

arXiv2019

The unbroken spectrum of Frobenius seaweeds II: type-B and type-C

Analogous to the Type-$A_{n-1}=\mathfrak{sl}(n)$ case, we show that if $\mathfrak{g}$ is a Frobenius seaweed subalgebra of $B_{n}=\mathfrak{so}(2n+1)$ or $C_{n}=\mathfrak{sp}(2n)$, then the spectrum of the adjoint of a principal element consists of an unbroken set of integers whose multiplicities have a symmetric distribution.

math.RT↗

arXiv2018

Observational determination of the galaxy bias from cosmic variance with a random pointing survey: Clustering of z~2 galaxies from Hubble's BoRG survey

Gravitational clustering broadens the count-in-cells distribution of galaxies for surveys along uncorrelated (well-separated) lines of sight beyond Poisson noise. A number of methods have proposed to measure this excess "cosmic" variance to constrain the galaxy bias (i.e. the strength of clustering) independently of the two-point correlation function. Here we present an observational application of these methods using data from 141 uncorrelated fields (~700 arcmin$^2$ total) from Hubble's Brightest of Reionizing Galaxies (BoRG) survey. We use BoRG's broad-band imaging in optical and near infrared to identify N~1000 photometric candidates at z~2 through a combination of colour selection and photometric redshift determination, building a magnitude-limited sample with $m_{AB}\leq24.5$ in F160W. We detect a clear excess in the variance of the galaxy number counts distribution compared to Poisson expectations, from which we estimate a galaxy bias $b \approx 3.63 \pm 0.57$. When divided by SED-fit classification into ~400 early-type and ~600 late-type candidates, we estimate biases of $b_{early} \approx 4.06 \pm 0.67$ and $b_{late} \approx 2.98 \pm 0.98$ respectively. These estimates are consistent with previous measurements of the bias from the two-point correlation function, and demonstrate that with $N\gtrsim100$ sight-lines, each containing $N\gtrsim5$ objects, the counts-in-cell analysis provides a robust measurement of the bias. This implies that the method can be applied effectively to determine clustering properties (and characteristic dark-matter halo masses) of z~6-9 galaxies from a pure-parallel James Webb Space Telescope survey similar in design to Hubble's BoRG survey.

astro-ph.GA↗

arXiv2017

An explicit edge-coloring of K_n with six colors on every K_5

For fixed integers p and q, let f(n,p,q) denote the minimum number of colors needed to color all of the edges of the complete graph K_n such that no clique of p vertices spans fewer than q distinct colors. A construction is given which shows that f(n,5,6) < n^(1/2+o(1)). This improves upon the best known probabilistic upper bound of O(n^(3/5)) given by Erd\H{o}s and Gy\'arf\'as. It is also shown that f(n,5,6) = {\Omega}(n^(1/2)).

math.CO↗

arXiv2017

A $(5,5)$-coloring of $K_n$ with few colors

For fixed integers $p$ and $q$, let $f(n,p,q)$ denote the minimum number of colors needed to color all of the edges of the complete graph $K_n$ such that no clique of $p$ vertices spans fewer than $q$ distinct colors. Any edge-coloring with this property is known as a $(p,q)$-coloring. We construct an explicit $(5,5)$-coloring that shows that $f(n,5,5) \leq n^{1/3 + o(1)}$ as $n \rightarrow \infty$. This improves upon the best known probabilistic upper bound of $O\left(n^{1/2}\right)$ given by Erd\H{o}s and Gy\'{a}rf\'{a}s, and comes close to matching the best known lower bound $\Omega\left(n^{1/3}\right)$.

math.CO↗

arXiv2016

Extremal Problems on Generalized Directed Hypergraphs

In this paper we define a class of combinatorial structures the instances of which can each be thought of as a model of directed hypergraphs in some way. Each of these models is uniform in that all edges have the same internal structure, and each is simple in that no loops or multiedges are allowed. We generalize the concepts of Turan density, blowup density, and jumps to this class and show that many basic extremal results extend naturally in this new setting. In particular, we show that supersaturation holds, the blowup of a generalized directed hypergraph (GDH) has the same Turan density as the GDH itself, and degenerate GDHs (those with Turan density zero) can be characterized as being contained in a blowup of a single edge. Additionally, we show how the set of jumps from one kind of GDH relates to the set of jumps of another. Since r-uniform hypergraphs are an instance of the defined class, then we are able to derive many particular instances of jumps and nonjumps for GDHs in general based on known results.

math.CO↗

arXiv2016

Extremal Numbers for 2 to 1 Directed Hypergraphs with Two Edges Part I: The Nondegenerate Cases

Let a 2 to 1 directed hypergraph be a 3-uniform hypergraph where every edge has two tail vertices and one head vertex. For any such directed hypergraph F let the nth extremal number of F be the maximum number of edges that any directed hypergraph on n vertices can have without containing a copy of F. There are actually two versions of this problem: the standard version where every triple of vertices is allowed to have up to all three possible directed edges and the oriented version where each triple can have at most one directed edge. In this paper, we determine the standard extremal numbers and the oriented extremal numbers for three different directed hypergraphs. Each has exactly two edges, and of the seven (nontrivial) 2 to 1 graphs with exactly two edges, these are the only three with extremal numbers that are cubic in n. The standard and oriented extremal numbers for the other four directed hypergraphs with two edges are determined in a companion paper.

math.CO↗