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Dirichlet-Neumann Operators (DNOs) are important to the formulation, analysis, and simulation of many crucial models found in engineering and the sciences. For instance, these operators permit moving-boundary problems, such as the classical water wave problem (free-surface ideal fluid flow under the influence of gravity and capillarity), to be restated in terms of interfacial quantities, which not only eliminates the boundary tracking problem, but also reduces the problem dimension. While these DNOs have been the object of much recent study regarding their numerical simulation and rigorous analysis, they have yet to be examined in the setting of laterally quasiperiodic boundary conditions. The purpose of this contribution is to begin this investigation with a particular eye towards the problem of more realistically simulating two and three dimensional surface water waves. Here we not only carefully define the DNO with respect to these boundary conditions for Laplace's equation, but we also show the rigorous analyticity of these operators with respect to sufficiently smooth boundary perturbations. These theoretical developments suggest a novel algorithm for the stable and high-order simulation of the DNO, which we implement and extensively test., Comment: 43 pages, 7 figures

Over the past twenty years, the field of plasmonics has been revolutionized with the isolation and utilization of two--dimensional materials, particularly graphene. Consequently there is significant interest in rapid, robust, and highly accurate computational schemes which can incorporate such materials. Standard volumetric approaches can be contemplated, but these require huge computational resources. Here we describe an algorithm which addresses this issue for nonlocal models of the electromagnetic response of graphene. Our methodology not only approximates the graphene layer with a surface current, but also reformulates the governing volumetric equations in terms of surface quantities using Dirichlet--Neumann Operators. We have recently shown how these surface equations can be numerically simulated in an efficient, stable, and accurate fashion using a High--Order Perturbation of Envelopes methodology. We extend these results to the nonlocal model mentioned above, and using an implementation of this algorithm, we study absorbance spectra of TM polarized plane--waves scattered by a periodic grid of graphene ribbons., Comment: 21 pages, 4 figures

Electromagnetic waves interacting with three--dimensional periodic structures occur in many applications of great scientific and engineering interest. These three dimensional interactions are extremely complicated and subtle, so it is unsurprising that practitioners find their rapid, robust, and accurate numerical simulation to be of paramount interest. Among the wide array of possible numerical approaches, the High--Order Spectral algorithms are often preferred due to their surpassing fidelity with a moderate number of unknowns, and here we describe an algorithm that fits into this class. In addition, we take a perturbative approach to the problem which views the deviation of the permittivity from a reference value as the deformation and we conduct a regular perturbation theory. This work concludes a line of research on these methods which began with two-dimensional problems governed by the Helmholtz equation and moved to small perturbations in the fully three-dimensional vector Maxwell equations. We now extend these latter results to large (real) perturbations constituting a rigorous analytic continuation., Comment: arXiv admin note: text overlap with arXiv:2307.15152

Photoionization models frequently assume constant temperature or density within HII regions. We investigate this assumption by measuring the detailed temperature and density structures of four HII regions in the Large Magellanic Cloud and the Small Magellanic Cloud, using integral-field spectroscopic data from the Wide-Field Spectrograph on the ANU 2.3m telescope. We analyse the distribution of emission-lines of low-ionization species, intermediate-ionization species and high-ionization species. We present the complex electron temperature and density structures within HII regions. All four nebulae present a negative gradient in the electron density profile. Both positive and negative temperature gradients are observed in the nebulae. We create a series of nebula models with a constant ISM pressure and varying temperature and density distributions. Comparison of the line ratios between our HII regions and models suggests that none of the simple nebula models can reproduce the observed temperature and density structures. Comparison between the models and the data suggests that the ISM pressure of nebulae in LMC and SMC is between log(P/k)=6-7.5. Complex internal structures of the nebulae highlight the importance of future Monte-Carlo photoionization codes for accurate nebula modeling, which include a comprehensive consideration of arbitrary geometries of HII regions., Comment: 24 pages, 12 figures, 11 tables, Accepted for publication in ApJ

The scattering of electromagnetic waves by three--dimensional periodic structures is important for many problems of crucial scientific and engineering interest. Due to the complexity and three-dimensional nature of these waves, the fast, accurate, and reliable numerical simulations of these are indispensable for engineers and scientists alike. For this, High Order Spectral methods are frequently employed and here we describe an algorithm in this class. Our approach is perturbative in nature where we view the deviation of the permittivity from a constant value as the deformation and we pursue regular perturbation theory. This work extends our previous contribution regarding the Helmholtz equation to the full vector Maxwell equations, by providing a rigorous analyticity theory, both in deformation size and spatial variable (provided that the permittivity is, itself, analytic)., Comment: 29

We use James Webb Space Telescope Near-Infrared Camera Wide Field Slitless Spectroscopy (NIRCam WFSS) and Near-Infrared spectrograph (NIRSpec) in the Cosmic Evolution Early Release survey (CEERS) to measure rest-frame optical emission-line of 155 galaxies at z>2. The blind NIRCam grism observations include a sample of galaxies with bright emission lines that were not observed on the NIRSpec masks. We study the changes of the Ha, [OIII]/Hb, and [NeIII]/[OII] emission lines in terms of redshift by comparing to lower redshift SDSS and CLEAR samples. We find a significant (>3$\sigma$) correlation between [OIII]/Hb with redshift, while [NeIII]/[OII] has a marginal (2$\sigma$) correlation with redshift. We compare [OIII]/Hb and [NeIII]/[OII] to stellar mass and Hb SFR. We find that both emission-line ratios have a correlation with Hb SFR and an anti-correlation with stellar mass across the redshifts 0

MACS0647$-$JD is a triply-lensed $z\sim11$ galaxy originally discovered with the Hubble Space Telescope. Here we report new JWST imaging, which clearly resolves MACS0647$-$JD as having two components that are either merging galaxies or stellar complexes within a single galaxy. Both are very small, with stellar masses $\sim10^8\,M_\odot$ and radii $r<100\,\rm pc$. The brighter larger component "A" is intrinsically very blue ($\beta\sim-2.6$), likely due to very recent star formation and no dust, and is spatially extended with an effective radius $\sim70\,\rm pc$. The smaller component "B" appears redder ($\beta\sim-2$), likely because it is older ($100-200\,\rm Myr$) with mild dust extinction ($A_V\sim0.1\,\rm mag$), and a smaller radius $\sim20\,\rm pc$. We identify galaxies with similar colors in a high-redshift simulation, finding their star formation histories to be out of phase. With an estimated stellar mass ratio of roughly 2:1 and physical projected separation $\sim400\,\rm pc$, we may be witnessing a galaxy merger 400 million years after the Big Bang. We also identify a candidate companion galaxy C $\sim3\,{\rm kpc}$ away, likely destined to merge with galaxies A and B. The combined light from galaxies A+B is magnified by factors of $\sim$8, 5, and 2 in three lensed images JD1, 2, and 3 with F356W fluxes $\sim322$, $203$, $86\,\rm nJy$ (AB mag 25.1, 25.6, 26.6). MACS0647$-$JD is significantly brighter than other galaxies recently discovered at similar redshifts with JWST. Without magnification, it would have AB mag 27.3 ($M_{UV}=-20.4$). With a high confidence level, we obtain a photometric redshift of $z=10.6\pm0.3$ based on photometry measured in 6 NIRCam filters spanning $1-5\rm\mu m$, out to $4300\,\r{A}$ rest-frame. JWST NIRSpec observations planned for January 2023 will deliver a spectroscopic redshift and a more detailed study of the physical properties of MACS0647$-$JD., Comment: 27 pages, 14 figures, accepted for publication in ApJL

Lyman Break Galaxy (LBG) candidates at z>10 are rapidly being identified in JWST/NIRCam observations. Due to the (redshifted) break produced by neutral hydrogen absorption of rest-frame UV photons, these sources are expected to drop out in the bluer filters while being well detected in redder filters. However, here we show that dust-enshrouded star-forming galaxies at lower redshifts (z<7) may also mimic the near-infrared (near-IR) colors of z>10 LBGs, representing potential contaminants in LBG candidate samples. First, we analyze CEERS-DSFG-1, a NIRCam dropout undetected in the F115W and F150W filters but detected at longer wavelengths. Combining the JWST data with (sub)millimeter constraints, including deep NOEMA interferometric observations, we show that this source is a dusty star-forming galaxy (DSFG) at z~5.1. We also present a tentative 2.6sigma SCUBA-2 detection at 850um around a recently identified z~16 LBG candidate in the same field and show that, if the emission is real and associated with this candidate, the available photometry is consistent with a z~5 dusty galaxy with strong nebular emission lines despite its blue near-IR colors. Further observations on this candidate are imperative to mitigate the low confidence of this tentative submillimeter emission and its positional uncertainty. Our analysis shows that robust (sub)millimeter detections of NIRCam dropout galaxies likely imply z=4-6 redshift solutions, where the observed near-IR break would be the result of a strong rest-frame optical Balmer break combined with high dust attenuation and strong nebular line emission, rather than the rest-frame UV Lyman break. This provides evidence that DSFGs may contaminate searches for ultra high-redshift LBG candidates from JWST observations., Comment: Published in The Astrophysical Journal Letters (updated to match the published version)

We report the discovery of a candidate galaxy with a photo-z of z~12 in the first epoch of the JWST Cosmic Evolution Early Release Science (CEERS) Survey. Following conservative selection criteria we identify a source with a robust z_phot = 11.8^+0.3_-0.2 (1-sigma uncertainty) with m_F200W=27.3, and >7-sigma detections in five filters. The source is not detected at lambda < 1.4um in deep imaging from both HST and JWST, and has faint ~3-sigma detections in JWST F150W and HST F160W, which signal a Ly-alpha break near the red edge of both filters, implying z~12. This object (Maisie's Galaxy) exhibits F115W-F200W > 1.9 mag (2-sigma lower limit) with a blue continuum slope, resulting in 99.6% of the photo-z PDF favoring z > 11. All data quality images show no artifacts at the candidate's position, and independent analyses consistently find a strong preference for z > 11. Its colors are inconsistent with Galactic stars, and it is resolved (r_h = 340 +/- 14 pc). Maisie's Galaxy has log M*/Msol ~ 8.5 and is highly star-forming (log sSFR ~ -8.2 yr^-1), with a blue rest-UV color (beta ~ -2.5) indicating little dust though not extremely low metallicity. While the presence of this source is in tension with most predictions, it agrees with empirical extrapolations assuming UV luminosity functions which smoothly decline with increasing redshift. Should followup spectroscopy validate this redshift, our Universe was already aglow with galaxies less than 400 Myr after the Big Bang., Comment: 17 pages, 6 figures, 3 tables, ApJL in press. Summary of changes from original submission: Improvements in astrometry generated a weak detection in F150W that reduces the photo-z to 11.8 but does not increase the likelihood of lower-z solutions. A full discussion of changes from the original version is available at: https://web.corral.tacc.utexas.edu/ceersdata/papers/Maisie_update.pdf

We present rest-frame optical emission-line flux ratio measurements for five $z>5$ galaxies observed by the JWST Near-Infared Spectrograph (NIRSpec) in the SMACS 0723 Early Release Observations. We add several quality-control and post-processing steps to the NIRSpec pipeline reduction products in order to ensure reliable relative flux calibration of emission lines that are closely separated in wavelength, despite the uncertain \textit{absolute} spectrophotometry of the current version of the reductions. Compared to $z\sim3$ galaxies in the literature, the $z>5$ galaxies have similar [OIII]$\lambda$5008/H$\beta$ ratios, similar [OIII]$\lambda$4364/H$\gamma$ ratios, and higher ($\sim$0.5 dex) [NeIII]$\lambda$3870/[OII]$\lambda$3728 ratios. We compare the observations to MAPPINGS V photoionization models and find that the measured [NeIII]$\lambda$3870/[OII]$\lambda$3728, [OIII]$\lambda$4364/H$\gamma$, and [OIII]$\lambda$5008/H$\beta$ emission-line ratios are consistent with an interstellar medium that has very high ionization ($\log(Q) \simeq 8-9$, units of cm~s$^{-1}$), low metallicity ($Z/Z_\odot \lesssim 0.2$), and very high pressure ($\log(P/k) \simeq 8-9$, units of cm$^{-3}$). The combination of [OIII]$\lambda$4364/H$\gamma$ and [OIII]$\lambda$(4960+5008)/H$\beta$ line ratios indicate very high electron temperatures of $4.1<\log(T_e/{\rm K})<4.4$, further implying metallicities of $Z/Z_\odot \lesssim 0.2$ with the application of low-redshift calibrations for ``$T_e$-based'' metallicities. These observations represent a tantalizing new view of the physical conditions of the interstellar medium in galaxies at cosmic dawn., Comment: Accepted for publication in AAS Journals. 14 pages, 6 figures, 3 tables

We use deep spectroscopy from the Hubble Space Telescope (HST) Wide-Field-Camera 3 (WFC3) IR grisms combined with broad-band photometry to study the stellar populations, gas ionization and chemical abundances in star-forming galaxies at $z\sim 1.1-2.3$. The data stem from the CANDELS Lyman-$\alpha$ Emission At Reionization (CLEAR) survey. At these redshifts the grism spectroscopy measure the [OII] 3727, 3729, [OIII] 4959, 5008, H-$\beta$ strong emission features, which constrain the ionization parameter and oxygen abundance of the nebular gas. We compare the line flux measurements to predictions from updated photoionization models (MAPPINGS (Kewley et al. 2019), which include an updated treatment of nebular gas pressure, log P/k = $n_e T_e$. Compared to low-redshift samples ($z\sim 0.2$) at fixed stellar mass, llog M / M$_\odot$ = 9.4-9.8, the CLEAR galaxies at z=1.35 (z=1.90) have lower gas-phase metallicity, $\Delta$(log Z) = 0.25 (0.35) dex, and higher ionization parameters, $\Delta$(log q) = 0.25 (0.35) dex, where U = q/c. We provide updated analytic calibrations between the [OIII], [OII], and H-$\beta$ emission line ratios, metallicity, and ionization parameter. The CLEAR galaxies show that at fixed stellar mass, the gas ionization parameter is correlated with the galaxy specific star-formation rates (sSFRs), where $\Delta$ log q = 0.4 $\Delta$(log sSFR), derived from changes in the strength of galaxy H-$\beta$ equivalent width. We interpret this as a consequence of higher gas densities, lower gas covering fractions, combined with higher escape fraction of H-ionizing photons. We discuss both tests to confirm these assertions and implications this has for future observations of galaxies at higher redshifts., Comment: 37 pages, plethora of figures, accepted for publication in ApJ. Updated with accepted version

We investigate how HII region temperature structure assumptions affect "direct-method" spatially-resolved metallicity observations using multispecies auroral lines in a galaxy from the SAMI Galaxy Survey. SAMI609396B, at redshift $z=0.018$, is a low-mass galaxy in a minor merger with intense star formation, analogous to conditions at high redshifts. We use three methods to derive direct metallicities and compare with strong-line diagnostics. The spatial metallicity trends show significant differences among the three direct methods. Our first method is based on the commonly used electron temperature $T_e$([OIII]) from the [OIII]$\lambda$4363 auroral line and a traditional $T_e$([OII]) -- $T_e$([OIII]) calibration. The second method applies a recent empirical correction to the O$^+$ abundance from the [OIII]/[OII] strong-line ratio. The third method infers the $T_e$([OII]) from the [SII]$\lambda\lambda$4069,76 auroral lines. The first method favours a positive metallicity gradient along SAMI609396B, whereas the second and third methods yield flattened gradients. Strong-line diagnostics produce mostly flat gradients, albeit with unquantified contamination from shocked regions. We conclude that overlooked assumptions about the internal temperature structure of HII regions in the direct method can lead to large discrepancies in metallicity gradient studies. Our detailed analysis of SAMI609396B underlines that high-accuracy metallicity gradient measurements require a wide array of emission lines and improved spatial resolutions in order to properly constrain excitation sources, physical conditions, and temperature structures of the emitting gas. Integral-field spectroscopic studies with future facilities such as JWST/NIRSpec and ground-based ELTs will be crucial in minimising systematic effects on measured gradients in distant galaxies., Comment: 21 pages, 14 figures, Accepted for Publication in MNRAS

For studies of galaxy formation and evolution, one of the major benefits of the James Webb Space Telescope is that space-based IFUs like those on its NIRSpec and MIRI instruments will enable spatially resolved spectroscopy of distant galaxies, including spectroscopy at the scale of individual star-forming regions in galaxies that have been gravitationally lensed. In the meantime, there is only a very small subset of lensed sources where work like this is possible even with the Hubble Space Telescope's Wide Field Camera 3 infrared channel grisms. We examine two of these sources, SDSS J1723+3411 and SDSS J2340+2947, using HST WFC3/IR grism data and supporting spatially-unresolved spectroscopy from several ground-based instruments to explore the size of spatial variations in observed strong emission line ratios like O32, R23, which are sensitive to ionization parameter and metallicity, and the Balmer decrement as an indicator of reddening. We find significant spatial variation in the reddening and the reddening-corrected O32 and R23 values which correspond to spreads of a few tenths of a dex in ionization parameter and metallicity. We also find clear evidence of a negative radial gradient in star formation in SDSS J2340+2947 and tentative evidence of one in SDSS J1723+3411, though its star formation is quite asymmetric. Finally, we find that reddening can vary enough spatially to make spatially-resolved reddening corrections necessary in order to characterize gradients in line ratios and the physical conditions inferred from them, necessitating the use of space-based IFUs for future work on larger, more statistically robust samples., Comment: 24 pages, including references, 6 tables, 17 figures, and appendix. Submitted to ApJ June 19, 2020