Seeding high-redshift QSOs by collisional runaway in primordial star clusters

We study how runaway stellar collisions in high-redshift, metal-poor star clusters form very massive stars (VMSs) that can directly collapse to intermediate-mass black holes (IMBHs). We follow the evolution of a pair of neighbouring high-redshift mini-haloes with high-resolution, cosmological hydrodynamical zoom-in simulations using the adaptive mesh refinement code RAMSES combined with the non-equilibrium chemistry package KROME. The first collapsing mini-halo is assumed to enrich the central nuclear star cluster (NSC) of the other to a critical metallicity, sufficient for Population II (Pop. II) star formation at redshift $z\approx27$. Using the spatial configuration of the flattened, asymmetrical gas cloud forming in the core of the metal enriched halo, we set the initial conditions for simulations of an initially non-spherical star cluster with the direct summation code NBODY6 which are compared to about 2000 NBODY6 simulations of spherical star clusters for a wide range of star cluster parameters. The final mass of the VMS that forms depends strongly on the initial mass and initial central density of the NSC. For the initial central densities suggested by our RAMSES simulations, VMSs with mass > 400 M$_{\odot}$ can form in clusters with stellar masses of $\approx10^4$ M$_{\odot}$, and this can increase to well over 1000 M$_{\odot}$ for more massive and denser clusters. The high probability we find for forming a VMS in these mini-haloes at such an early cosmic time makes collisional runaway of Pop. II star clusters a promising channel for producing large numbers of high-redshift IMBHs that may act as the seeds of supermassive black holes

Approaches to analysis with infinitesimals following Robinson, Nelson, and others

This is a survey of several approaches to the framework for working with infinitesimals and infinite numbers, originally developed by Abraham Robinson in the 1960s, and their constructive engagement with the Cantor-Dedekind postulate and the Intended Interpretation hypothesis. We highlight some applications including (1) Loeb's approach to the Lebesgue measure, (2) a radically elementary approach to the vibrating string, (3) true infinitesimal differential geometry. We explore the relation of Robinson's and related frameworks to the multiverse view as developed by Hamkins. Keywords: axiomatisations, infinitesimal, nonstandard analysis, ultraproducts, superstructure, set-theoretic foundations, multiverse, naive integers, intuitionism, soritical properties, ideal elements, protozoa

From Nonstandard Analysis to various flavours of Computability Theory

As suggested by the title, it has recently become clear that theorems of Nonstandard Analysis (NSA) give rise to theorems in computability theory (no longer involving NSA). Now, the aforementioned discipline divides into classical and higher-order computability theory, where the former (resp. the latter) sub-discipline deals with objects of type zero and one (resp. of all types). The aforementioned results regarding NSA deal exclusively with the higher-order case; we show in this paper that theorems of NSA also give rise to theorems in classical computability theory by considering so-called textbook proofs.Comment: To appear in the proceedings of TAMC2017 (http://tamc2017.unibe.ch/

New Methods for Identifying Lyman Continuum Leakers and Reionization-Epoch Analogues

Identifying low-redshift galaxies that emit Lyman continuum radiation (LyC leakers) is one of the primary, indirect methods of studying galaxy formation in the epoch of reionization. However, not only has it proved challenging to identify such systems, it also remains uncertain whether the low-redshift LyC leakers are truly ‘analogues’ of the sources that reionized the Universe. Here, we use high-resolution cosmological radiation hydrodynamics simulations to examine whether simulated galaxies in the epoch of reionization share similar emission line properties to observed LyC leakers at z ∼ 3 and z ∼ 0. We find that the simulated galaxies with high LyC escape fractions (fesc) often exhibit high O32 and populate the same regions of the R23–O32 plane as z ∼ 3 LyC leakers. However, we show that viewing angle, metallicity, and ionization parameter can all impact where a galaxy resides on the O32–fesc plane. Based on emission line diagnostics and how they correlate with fesc, lower metallicity LyC leakers at z ∼ 3 appear to be good analogues of reionization-era galaxies. In contrast, local [S II]-deficient galaxies do not overlap with the simulated high-redshift LyC leakers on the S II Baldwin–Phillips–Terlevich (BPT) diagram; however, this diagnostic may still be useful for identifying leakers. We use our simulated galaxies to develop multiple new diagnostics to identify LyC leakers using infrared and nebular emission lines. We show that our model using only [C II]158 μm and [O III]88 μm can identify potential leakers from non-leakers from the local Dwarf Galaxy Survey. Finally, we apply this diagnostic to known high-redshift galaxies and find that MACS 1149_JD1 at z = 9.1 is the most likely galaxy to be actively contributing to the reionization of the Universe

Probing cosmic dawn with emission lines: predicting infrared and nebular line emission for ALMA and JWST

Infrared and nebular lines provide some of our best probes of the physics regulating the properties of the interstellar medium (ISM) at high-redshift. However, interpreting the physical conditions of high-redshift galaxies directly from emission lines remains complicated due to inhomogeneities in temperature, density, metallicity, ionisation parameter, and spectral hardness. We present a new suite of cosmological, radiation-hydrodynamics simulations, each centred on a massive Lyman-break galaxy that resolves such properties in an inhomogeneous ISM. Many of the simulated systems exhibit transient but well defined gaseous disks that appear as velocity gradients in [CII]~158.6$\mu$m emission. Spatial and spectral offsets between [CII]~158.6$\mu$m and [OIII]~88.33$\mu$m are common, but not ubiquitous, as each line probes a different phase of the ISM. These systems fall on the local [CII]-SFR relation, consistent with newer observations that question previously observed [CII]~158.6$\mu$m deficits. Our galaxies are consistent with the nebular line properties of observed $z\sim2-3$ galaxies and reproduce offsets on the BPT and mass-excitation diagrams compared to local galaxies due to higher star formation rate (SFR), excitation, and specific-SFR, as well as harder spectra from young, metal-poor binaries. We predict that local calibrations between H$\alpha$ and [OII]~3727$\AA$ luminosity and galaxy SFR apply up to $z>10$, as do the local relations between certain strong line diagnostics (R23 and [OIII]~5007$\AA$/H$\beta$) and galaxy metallicity. Our new simulations are well suited to interpret the observations of line emission from current (ALMA and HST) and upcoming facilities (JWST and ngVLA)

Cycle-centrality in complex networks

Networks are versatile representations of the interactions between entities in complex systems. Cycles on such networks represent feedback processes which play a central role in system dynamics. In this work, we introduce a measure of the importance of any individual cycle, as the fraction of the total information flow of the network passing through the cycle. This measure is computationally cheap, numerically well-conditioned, induces a centrality measure on arbitrary subgraphs and reduces to the eigenvector centrality on vertices. We demonstrate that this measure accurately reflects the impact of events on strategic ensembles of economic sectors, notably in the US economy. As a second example, we show that in the protein-interaction network of the plant Arabidopsis thaliana, a model based on cycle-centrality better accounts for pathogen activity than the state-of-art one. This translates into pathogen-targeted-proteins being concentrated in a small number of triads with high cycle-centrality. Algorithms for computing the centrality of cycles and subgraphs are available for download

New methods for identifying Lyman continuum leakers and reionization-epoch analogues

Identifying low-redshift galaxies that emit Lyman Continuum radiation (LyC leakers) is one of the primary, indirect methods of studying galaxy formation in the epoch of reionization. However, not only has it proved challenging to identify such systems, it also remains uncertain whether the low-redshift LyC leakers are truly "analogues" of the sources that reionized the Universe. Here, we use high-resolution cosmological radiation hydrodynamics simulations to examine whether simulated galaxies in the epoch of reionization share similar emission line properties to observed LyC leakers at $z\sim3$ and $z\sim0$. We find that the simulated galaxies with high LyC escape fractions ($f_{\rm esc}$) often exhibit high O32 and populate the same regions of the R23-O32 plane as $z\sim3$ LyC leakers. However, we show that viewing angle, metallicity, and ionisation parameter can all impact where a galaxy resides on the O32-$f_{\rm esc}$ plane. Based on emission line diagnostics and how they correlate with $f_{\rm esc}$, lower-metallicity LyC leakers at $z\sim3$ appear to be good analogues of reionization-era galaxies. In contrast, local [SII]-deficient galaxies do not overlap with the simulated high-redshift LyC leakers on the SII-BPT diagram; however, this diagnostic may still be useful for identifying leakers. We use our simulated galaxies to develop multiple new diagnostics to identify LyC leakers using IR and nebular emission lines. We show that our model using only [CII]$_{\rm 158\mu m}$ and [OIII]$_{\rm 88\mu m}$ can identify potential leakers from non-leakers from the local Dwarf Galaxy Survey. Finally, we apply this diagnostic to known high-redshift galaxies and find that MACS1149_JD1 at $z=9.1$ is the most likely galaxy to be actively contributing to the reionization of the Universe

Tracing the sources of reionization in cosmological radiation hydrodynamics simulations

We use the photon flux and absorption tracer algorithm presented in Katz et al.~2018, to characterise the contribution of haloes of different mass and stars of different age and metallicity to the reionization of the Universe. We employ a suite of cosmological multifrequency radiation hydrodynamics AMR simulations that are carefully calibrated to reproduce a realistic reionization history and galaxy properties at $z \geq 6$. In our simulations, haloes with mass $10^9{\rm M_{\odot}}h^{-1}<M<10^{10}{\rm M_{\odot}}h^{-1}$, stars with metallicity $10^{-3}Z_{\odot}<Z<10^{-1.5}Z_{\odot}$, and stars with age $3\,{\rm Myr} < t < 10 \, {\rm Myr}$ dominate reionization by both mass and volume. We show that the sources that reionize most of the volume of the Universe by $z=6$ are not necessarily the same sources that dominate the meta-galactic UV background at the same redshift. We further show that in our simulations, the contribution of each type of source to reionization is not uniform across different gas phases. The IGM, CGM, filaments, ISM, and rarefied supernova heated gas have all been photoionized by different classes of sources. Collisional ionisation contributes at both the lowest and highest densities. In the early stages of the formation of individual HII bubbles, reionization proceeds with the formation of concentric shells of gas ionised by different classes of sources, leading to large temperature variations as a function of galacto-centric radius. The temperature structure of individual HII bubbles may thus give insight into the star formation history of the galaxies acting as the first ionising sources. Our explorative simulations highlight how the complex nature of reionization can be better understood by using our photon tracer algorithm

Higher order QCD corrections to charged-lepton deep-inelastic scattering and global fits of parton distributions

We study the perturbative QCD corrections to heavy-quark structure functions of charged-lepton deep-inelastic scattering and their impact on global fits of parton distributions. We include the logarithmically enhanced terms near threshold due to soft gluon resummation in the QCD corrections at next-to-next-to-leading order. We demonstrate that this approximation is sufficient to describe the available HERA data in most parts of the kinematic region. The threshold-enhanced next-to-next-to-leading order corrections improve the agreement between predictions based on global fits of the parton distribution functions and the HERA collider data even in the small-x region.Comment: 11 pages, 6 figures, latex, extended journal versio

The nature of high [O III]88 μ m/[C II]158 μm galaxies in the epoch of reionization: Low carbon abundance and a top-heavy IMF?

ALMA observations of z > 6 galaxies have revealed abnormally high [O III]88 μm/[C II]158 μm ratios and [C II]158 μm deficits compared to local galaxies. The origin of this behaviour is unknown. Numerous solutions have been proposed including differences in C and O abundance ratios, observational bias, and differences in ISM properties, including ionization parameter, gas density, or photodissociation region (PDR) covering fraction. In order to elucidate the underlying physics that drives this high-redshift phenomenon, we employ SPHINX20, a state-of-the-art, cosmological radiation–hydrodynamics simulation, that resolves detailed ISM properties of thousands of galaxies in the epoch of reionization which has been post-processed with CLOUDY to predict emission lines. We find that the observed z > 6 [O III]88 μm–SFR and [C II]158 μm–SFR relations can only be reproduced when the C/O abundance ratio is ∼8 × lower than Solar and the total metal production is ∼4 × higher than that of a Kroupa IMF. This implies that high-redshift galaxies are potentially primarily enriched by low-metallicity core–collapse supernovae with a more top-heavy IMF. As AGB stars and type-Ia supernova begin to contribute to the galaxy metallicity, both the [C II]158 μm–SFR and [C II]158 μm luminosity functions are predicted to converge to observed values at z ∼ 4.5. While we demonstrate that ionization parameter, LyC escape fraction, ISM gas density, and CMB attenuation all drive galaxies towards higher [O III]88 μm/[C II]158 μm, observed values at z > 6 can only be reproduced with substantially lower C/O abundances compared to Solar. The combination of [C II]158 μm and [O III]88 μm can be used to predict the values of ionization parameter, ISM gas density, and LyC escape fraction and we provide estimates of these quantities for nine observed z > 6 galaxies. Finally, we demonstrate that [O I]63 μm can be used as a replacement for [C II]158 μ m in high-redshift galaxies where [C II]158 μ m is unobserved and argue that more observation time should be used to target [O I]63 μm at z > 6. Future simulations will be needed to self-consistently address the numerous uncertainties surrounding a varying IMF at high redshift and the associated metal returns