Search

We obtain formulae for the numbers of isomorphism and conjugacy classes of non-identity proper subgroups of the groups $G={\rm PSL}_2(p)$, $p$ prime, and for the numbers of those conjugacy classes which do or do not consist of self-normalising subgroups. The formulae are used to prove lower bounds $17$, $18$, $6$ and $12$ respectively satisfied by these invariants for all $p>37$. A computer search carried out for a different problem shows that these bounds are attained for over a million primes $p$; we show that if the Bateman--Horn Conjecture is true, they are attained for infinitely many primes. Also, assuming no unproved conjectures, we use a result of Heath-Brown to obtain upper bounds for these invariants, valid for an infinite set of primes $p$., Comment: 10 pages

The James Webb Space Telescope is revolutionising our ability to understand the host galaxies and local environments of high-z quasars. Here we obtain a comprehensive understanding of the host galaxy of the z=7.08 quasar J1120+0641 by combining NIRSpec integral field spectroscopy with NIRCam photometry of the host continuum emission. Our emission line maps reveal that this quasar host is undergoing a merger with a bright companion galaxy. The quasar host and the companion have similar dynamical masses of $\sim10^{10}M_\odot$, suggesting that this is a major galaxy interaction. Through detailed quasar subtraction and SED fitting using the NIRCam data, we obtain an estimate of the host stellar mass of $M_{\ast}\simeq2.6\times10^9M_\odot$, with $M_{*}\simeq5.0\times10^9M_\odot$ for the companion galaxy. Using the H$\beta$ Balmer line we estimate a virial black hole mass of $M_{\rm{BH}}\simeq1.4\times10^9 M_\odot$. Thus, J1120+0641 has an extreme black hole - stellar mass ratio of $M_{\rm{BH}}/M_\ast\simeq0.54$, which is ~3 dex larger than expected by the local scaling relations between black hole and stellar mass. J1120+0641 is powered by an overmassive black hole with the highest reported black hole - stellar mass ratio, in a quasar host that is currently undergoing a major merger -- these new insights highlight the power of JWST for measuring and understanding these extreme first quasars., Comment: Submitted to A&A, comments welcome

This paper is a report of the Workshop on Simulations for Information Access (Sim4IA) workshop at SIGIR 2024. The workshop had two keynotes, a panel discussion, nine lightning talks, and two breakout sessions. Key takeaways were user simulation's importance in academia and industry, the possible bridging of online and offline evaluation, and the issues of organizing a companion shared task around user simulations for information access. We report on how we organized the workshop, provide a brief overview of what happened at the workshop, and summarize the main topics and findings of the workshop and future work., Comment: Preprint of a SIGIR Forum submission for Vol. 58 No. 2 - December 2024

For the first time, we systematically search for galaxies with extended emission line and potential outflows features using medium-band images in the GOODS-S field by comparing the morphology in medium-band images to adjacent continuum and UV bands. We look for galaxies that have a maximum extent 50\% larger, an excess area 30\% greater, or an axis ratio difference of more than 0.3 in the medium band compared to the reference bands. After visual inspection, we find 326 candidate galaxies at $1 < z < 6$, with a peak in the population near cosmic noon, benefiting from the good coverage of the medium-band filters. By examining their SEDs, we find that the candidate galaxies are at least 20\% more bursty in their star-forming activity and have 60\% more young stellar populations compared to a control sample selected based on the continuum band flux. Additionally, these candidates exhibit a significantly higher production rate of ionizing photons. We further find that candidates hosting known AGN produce extended emission that is more anisotropic compared to non-AGN candidates. A few of our candidates have been spectroscopically confirmed to have prominent outflow signatures through NIRSpec observations, showcasing the robustness of the photometric selection. Future spectroscopic follow-up will better help verify and characterize the kinematics and chemical properties of these systems., Comment: 21 pages, 12 figures, 2 tables. Submitted to AAS journals

Spin-photon interfaces based on group-IV colour centres in diamond offer a promising platform for quantum networks. A key challenge in the field is realizing precise single-defect positioning and activation, which is crucial for scalable device fabrication. Here we address this problem by demonstrating a two-step fabrication method for tin vacancy (SnV-) centres that uses site-controlled ion implantation followed by local femtosecond laser annealing with in-situ spectral monitoring. The ion implantation is performed with sub-50 nm resolution and a dosage that is controlled from hundreds of ions down to single ions per site, limited by Poissonian statistics. Using this approach, we successfully demonstrate site-selective creation and modification of single SnV- centres. The technique opens a window onto materials tuning at the single defect level, and provides new insight into defect structures and dynamics during the annealing process. While demonstrated for SnV- centres, this versatile approach can be readily generalised to other implanted colour centres in diamond and wide-bandgap materials., Comment: 10 pages, 4 figures, methods, and supplementary information

Ly$\alpha$ is the transition to the ground state from the first excited state of hydrogen (the most common element). Resonant scattering of this line by neutral hydrogen greatly impedes its emergence from galaxies, so the fraction of galaxies which show Ly$\alpha$ is a tracer of the neutral fraction of the intergalactic medium (IGM), and thus the history of reionization. In previous works, we used early JWST/NIRSpec data from the JWST Advanced Deep Extragalactic Survey (JADES) to classify and characterise Ly$\alpha$ emitting galaxies (LAEs). This survey is now approaching completion, and the current sample is nearly an order of magnitude larger. From a sample of 784 galaxies in JADES at $4.0

$\require{mediawiki-texvc}$Cosmic Reionisation commenced when ultraviolet (UV) radiation produced in the first galaxies began illuminating the cold, neutral gas that filled the primordial Universe. Recent James Webb Space Telescope (JWST) observations have shown that surprisingly UV-bright galaxies were in place beyond redshift $z = 14$, when the Universe was less than 300 Myr old. Smooth turnovers of their UV continua have been interpreted as damping-wing absorption of Lyman-$\alpha$ (Ly$\alpha$), the principal hydrogen transition. However, spectral signatures encoding crucial properties of these sources, such as their emergent radiation field, largely remain elusive. Here we report spectroscopy from the JWST Advanced Deep Extragalactic Survey (JADES) of a galaxy at redshift $z = 13.0$ that reveal a singular, bright emission line unambiguously identified as Ly$\alpha$, in addition to a smooth turnover. We observe an equivalent width of $\text{EW}_\mathrm{Ly\alpha} > 40 \, \AA$ (rest frame), previously only seen at $z < 9$ where the intervening intergalactic medium (IGM) becomes increasingly ionised. Together with a very blue UV continuum, the Ly$\alpha$ line indicates the galaxy is a prolific producer of ionising photons, a significant fraction of which may escape. This suggests it resides in an early reionised region preventing complete extinction of Ly$\alpha$, thus shedding new light on the nature of the earliest galaxies and the onset of Reionisation only 330 Myr after the Big Bang., Comment: 19 pages, 9 figures, 3 tables. Comments welcome

We present NIRSpec/MSA observations from the JWST large-area survey WIDE, targeting the rest-frame UV-optical spectrum of Ulema, a radio-AGN host at redshift z=4.6348. The low-resolution prism spectrum displays high equivalent width nebular emission, with remarkably high ratios of low-ionisation species of oxygen, nitrogen and sulphur, relative to hydrogen; auroral O$^+$ emission is clearly detected, possibly also C$^+$. From the high-resolution grating spectrum, we measure a gas velocity dispersion $\sigma$~400 km s$^{-1}$, broad enough to rule out star-forming gas in equilibrium in the gravitational potential of the galaxy. Emission-line ratio diagnostics suggest that the nebular emission is due to a shock which ran out of pre-shock gas. To infer the physical properties of the system, we model simultaneously the galaxy spectral energy distribution (SED) and shock-driven line emission under a Bayesian framework. We find a relatively low-mass, star-forming system (M* = 1.4$\times$10^{10} M$_\odot$, SFR = 70 M$_\odot$ yr$^{-1}$), where shock-driven emission contributes 50 per cent to the total H$\beta$ luminosity. The nebular metallicity is near solar - three times higher than that predicted by the mass-metallicity relation at z=4.6, possibly related to fast-paced chemical evolution near the galaxy nucleus. We find no evidence for a recent decline in the SFR of the galaxy, meaning that, already at this early epoch, fast radio-mode AGN feedback was poorly coupled with the bulk of the star-forming gas; therefore, most of the feedback energy must end up in the galaxy halo, setting the stage for future quenching., Comment: 20 pages, 10 figures, 4 tables. Submitted to MNRAS, comments welcome

Galactic outflows driven by star formation or active galactic nuclei are typically formed by multi-phase gas whose temperature spans over 4 orders of magnitude. Probing the different outflow components requires multi-wavelength observations and long exposure times, especially in the distant Universe. So far, most of the high-z studies have focused on a single gas phase, but this kind of analysis may potentially miss a non-negligible fraction of the total outflowing gas content. In this work, we analyze the spatially resolved rest-frame UV and optical emission from HZ4, the highest redshift main sequence star-forming galaxy having a detected [C II] outflow, which traces the neutral gas component. Our goal is to study the ionized interstellar medium in the galaxy and the properties of the ionized outflow as traced by the [O III]$\lambda$5007\r{A} and H$\alpha$ emission lines. We exploit JWST/NIRSpec observations in the integral field spectroscopy mode to investigate the galaxy properties by making use of the brightest rest-frame optical emission lines. Their high spectral and spatial resolution allows us to trace the ionized outflow from broad line wings and spatially resolve it. We also re-analyze the [C II] ALMA data to compare the neutral atomic and ionized outflow morphologies, masses, and energetics. We find that the system consists of a galaxy merger, instead of a rotating disk as originally inferred from low-resolution [C II] observations, and hosts an extended ionized outflow. The ionized outflow is being launched from a region hosting an intense burst of star formation and extends over 4 kpc from the launch site. The neutral and ionized outflows are almost co-spatial, but the mass loading factor in the ionized gas phase is two orders of magnitude smaller than in the neutral phase, as found for other lower redshift multi-phase outflows., Comment: 22 pages, 20 figures, submitted to A&A

We present JWST/NIRSpec integral-field spectroscopy observations of the z ~ 9.11 lensed galaxy MACS1149-JD1, as part of the GA-NIFS programme. The data was obtained with both the G395H grating (R~ 2700) and the prism (R~ 100). This target shows a main elongated UV-bright clump and a secondary component detected in continuum emission at a projected distance of 2 kpc. The R2700 data trace the ionised-gas morpho-kinematics in between the two components, showing an elongated emission mainly traced by [O III]5007. We spatially resolve [O II]3726,3729, [O III]4959,5007, and [O III]4363, which enable us to map the electron density (ne ~ 1.0 x 103 cm-3), temperature (Te ~ 1.6 x 104 K), and direct-method gas-phase metallicity (-1.2 to -0.7 dex solar). A spatially resolved full-spectrum modelling of the prism indicates a north-south gas metallicity and stellar age gradient between the two components. We found 3-sigma evidence of a spatially resolved anti-correlation of the gas-phase metallicity and the star formation rate density, which is likely driven by gas inflows, enhancing the star formation in JD1. We employ high-z sensitive diagnostic diagrams to rule out the presence of a strong AGN in the main component. These findings show the unambiguous presence of two distinct stellar populations, with the majority of the mass ascribed to an old star formation burst, as suggested by previous works. We disfavour the possibility of a rotating-disc nature for MACS1149-JD1; we favour a merger event that has led to a recent burst of star formation in two separate regions, as supported by high values of [O III]5007/Hbeta, ionised gas velocity dispersion, and gas-phase metallicity., Comment: 14 pages, 16 figures

We investigate the physical properties of Lyman-alpha emitters (LAEs) and non-Lyman-alpha emitters (non-LAEs) at z$\sim$4.8--9.6 via a stacking analysis of 253 JWST/NIRSpec spectra of galaxies observed as part of the JWST Advanced Deep Extragalactic Survey (JADES). We identify a sample of 42 LAEs with the equivalent width of Ly$\alpha$ $\gtrsim$20\AA and a sample of 211 non-LAEs, divide each sample further via the median redshift of the LAEs (z~6.3), and create composite spectra using the low and medium resolution spectra from NIRSpec. We estimate physical quantities such as dust extinction, UV continuum slope $\beta$, electron temperatures, ionization parameter, escape fraction of Ly$\alpha$ and Lyman Continuum, and the photon production rate for each bin/stack. The existing dust-extinction laws do not appear to be valid at these epochs. The emission line ratio analyses show that active galactic nuclei might dominate all sub-samples, irrespective of Ly$\alpha$ emission. LAEs show much higher [OIII]/[OII] and low [OII]/H$\delta$ at z$\lesssim$6.3 compared to non-LAEs, but these line ratios are not sufficient to distinguish the two populations at z$>$6.3. However, the LAEs samples show large EW([OIII]4959, 5007) ($>$1000\AA) compared to the non-LAEs sample at all redshifts. CIV/Ly$\alpha$ and CIV/CIII] for LAE population at z$\lesssim$6.3 is $\sim$a factor of 5 larger than that for LAE population at z$>$6.3. The ionizing radiation for LAEs is hard, as revealed from several diagnostics, including CIV detection, high [OIII]/[OII] ($>$8), and large values of $\xi^{\star}_{ion}$., Comment: Submitted to ApJ, 20 pages, 13 figures, 2 tables

We present JWST NIRSpec observations in IFS mode of the galaxy GS5001 at redshift z=3.47, the brightest member of a candidate protocluster in the GOODS-S field. The data cover a field of view (FoV) of 4''$\times$4'' (~$30\times30$~kpc$^2$) and were obtained as part of the GA-NIFS GTO program. The observations include both high (R~2700) and low (R~100) spectral resolution data, spanning the rest-frame wavelength ranges 3700-6780A and 1300-11850A, respectively. We analyse the spatially resolved ionised gas kinematics and interstellar medium properties, including obscuration, gas metallicity, excitation, ionisation parameter, and electron density. In addition to the central galaxy, the NIRSpec FoV covers three components in the south, with velocities blue-shifted by -150 km/s with respect to the main galaxy, and another source in the north redshifted by ~200 km/s. The emission line ratios in the BPT diagram are consistent with star formation for all the sources in the FoV. We measure electron densities of ~500 cm$^{-3}$ in the different sources. The gas-phase metallicity in the main galaxy is 12+log(O/H) $= 8.45\pm0.04$, and slightly lower in the companions (12+log(O/H)$ = 8.34-8.42$), consistent with the mass-metallicity relation at $z\sim3$. We find peculiar line ratios (high log [NII]/H$\alpha$, low log [OIII]/H$\beta$) in the northern part of the main galaxy (GS5001). These could be attributed to either higher metallicity, or to shocks resulting from the interaction of the main galaxy with the northern source. We identify a spatially resolved outflow in the main galaxy, with an extension of about 3 kpc. We find maximum outflow velocities of ~400 km/s, an outflow mass of $(1.7\pm0.4)\times 10^8$ M$_{\odot}$, a mass outflow rate of $23\pm5$ M$_{\odot}$ yr$^{-1}$ and a mass loading factor of 0.23. These properties are compatible with star formation being the driver of the outflow., Comment: Submitted to A&A

JWST is discovering increasing numbers of quiescent galaxies 1--2 billion years after the Big Bang, whose redshift, high mass, and old stellar ages indicate that their formation and quenching were surprisingly rapid. This fast-paced evolution seems to require that feedback from AGN (active galactic nuclei) be faster and/or more efficient than previously expected \citep{Xie24}. We present deep ALMA observations of cold molecular gas (the fuel for star formation) in a massive, fast-rotating, post-starburst galaxy at $z=3.064$. This galaxy hosts an AGN, driving neutral-gas outflows with a mass-outflow rate of $60\pm20$ M$_{\odot}$ yr$^{-1}$, and has a star-formation rate of $<5.6$ M$_{\odot}$ yr$^{-1}$. Our data reveal this system to be the most distant gas-poor galaxy confirmed with direct CO observations (molecular-gas mass $< 10^{9.1}$ M$_{\odot}$; <0.8 % of its stellar mass). Combining ALMA and JWST observations, we estimate the gas-consumption history of this galaxy, showing that it evolved with net zero gas inflow, i.e., gas consumption by star formation matches the amount of gas this galaxy is missing relative to star-forming galaxies. This could arise both from preventive feedback stopping further gas inflow, which would otherwise refuel star formation or, alternatively, from fine-tuned ejective feedback matching precisely gas inflows. Our methods, applied to a larger sample, promise to disentangle ejective vs preventive feedback., Comment: 14 pages, 4 figures

The first observations of JWST have revolutionized our understanding of the Universe by identifying for the first time galaxies at $z\sim13$. In addition, the discovery of many luminous galaxies at Cosmic Dawn ($z>10$) has suggested that galaxies developed rapidly, in apparent tension with many standard models. However, most of these galaxies lack spectroscopic confirmation, so their distances and properties are uncertain. We present JADES JWST/NIRSpec spectroscopic confirmation of two luminous galaxies at redshifts of $z=14.32^{+0.08}_{-0.20}$ and $z=13.90\pm0.17$. The spectra reveal ultraviolet continua with prominent Lyman-$\alpha$ breaks but no detected emission lines. This discovery proves that luminous galaxies were already in place 300~million years after the Big Bang and are more common than what was expected before JWST. The most distant of the two galaxies is unexpectedly luminous and is spatially resolved with a radius of 260 parsecs. Considering also the very steep ultraviolet slope of the second galaxy, we conclude that both are dominated by stellar continuum emission, showing that the excess of luminous galaxies in the early Universe cannot be entirely explained by accretion onto black holes. Galaxy formation models will need to address the existence of such large and luminous galaxies so early in cosmic history., Comment: 15 figures, 3 tables, published in Nature

The James Webb Space Telescope (JWST) has spectroscopically confirmed numerous galaxies at $z > 10$. While weak rest-ultraviolet emission lines have only been seen in a handful of sources, the stronger rest-optical emission lines are highly diagnostic and accessible at mid-infrared wavelengths with the Mid-Infrared Instrument (MIRI) of JWST. We report the photometric detection of the most distant spectroscopically confirmed galaxy JADES-GS-z14-0 at $z = 14.32^{+0.08}_{-0.20}$ with MIRI at $7.7\ \mu\mathrm{m}$. The most plausible solution for the stellar population properties is that this galaxy contains half a billion solar masses in stars with a strong burst of star formation in the most recent few million years. For this model, at least one-third of the flux at $7.7\ \mu\mathrm{m}$ comes from the rest-optical emission lines $\mathrm{H}\beta$ and/or $\mathrm{[OIII]}\lambda\lambda4959,5007$. The inferred properties of JADES-GS-z14-0 suggest rapid mass assembly and metal enrichment during the earliest phases of galaxy formation., Comment: Submitted; main text has 9 pages, 3 figures and 1 table; extended text has 15 pages, 5 figures, and 1 table

We present observations of the $z\sim5.7$ Lyman-break galaxy HZ10 with the JWST/NIRSpec IFU in high and low spectral resolution (G395H, $R\sim2700$ and PRISM, $R\sim100$, respectively), as part of the GA-NIFS program. By spatially resolving the source, we find evidence for three spatially and spectrally distinct regions of line emission along with one region of strong continuum emission, all within a projected distance of $<10$kpc. The R2700 data features strong detections in H$\beta$, [OIII]$\lambda\lambda4959{,}5007$, [NII]$\lambda\lambda6548{,}6584$, H$\alpha$, and [SII]$\lambda\lambda6716{,}6731$. The R100 data additionally contains a strong detection of the Ly$\alpha$ break, rest-UV continuum, and [OII]$\lambda\lambda3726{,}3729$. None of the detected lines present strong evidence for AGN excitation from line diagnostic diagrams, and no high-ionisation lines are detected. Using the detected lines, we constrain the electron density $\left( \rm \log_{10}\left( n_e / cm^{-3}\right)\sim2.5-3.3\right)$ and metallicity ($\sim0.5-0.7$ solar) in each component. Spaxel-by-spaxel fits of each cube reveal a strong east-west velocity gradient and significant line asymmetries (indicating tidal features or outflows). The western component features a very red UV slope ($\beta_{UV}\sim-1$) and significant H$\alpha$ emission, suggesting an evolved population and active star formation. From a comparison to high resolution [CII]$158\mu$m imaging obtained with the Atacama Large Millimetre/submillimetre Array (ALMA), we find that the continuum emitter is associated with a gas-poor stellar population. Altogether, these data suggest that HZ10 represents an ongoing merger, with a complex distribution of stars, gas, and dust $<1$Gyr after the Big Bang., Comment: 16 pages, 11 figures. Submitted to MNRAS

We present the third data release of JADES, the JWST Advanced Deep Extragalactic Survey, providing both imaging and spectroscopy in the two GOODS fields. Spectroscopy consists of medium-depth and deep NIRSpec/MSA spectra of 4,000 targets, covering the spectral range 0.6-5.3 $\mu$m and observed with both the low-dispersion prism (R=30-300) and all three medium-resolution gratings (R=500-1,500). We describe the observations, data reduction, sample selection, and target allocation. We measured 2,375 redshifts (2,053 from multiple emission lines); our targets span the range from z=0.5 up to z=13, including 404 at z>5. The data release includes 2-d and 1-d fully reduced spectra, with slit-loss corrections and background subtraction optimized for point sources. We also provide redshifts and S/N>5 emission-line flux catalogs for the prism and grating spectra, and concise guidelines on how to use these data products. Alongside spectroscopy, we are also publishing fully calibrated NIRCam imaging, which enables studying the JADES sample with the combined power of imaging and spectroscopy. Together, these data provide the largest statistical sample to date to characterize the properties of galaxy populations in the first billion years after the Big Bang., Comment: 41 pages, 26 figures, 10 tables. Submitted to ApJS

$\require{mediawiki-texvc}$Given the sensitivity of the resonant Lyman-$\mathrm{\alpha}$ (Ly$\mathrm{\alpha}$) transition to absorption by neutral hydrogen, observations of Ly$\mathrm{\alpha}$ emitting galaxies (LAEs) have been widely used to probe the ionising capabilities of reionisation-era galaxies and their impact on the intergalactic medium (IGM). However, prior to JWST our understanding of the contribution of fainter sources and of ionised `bubbles' at earlier stages of reionisation remained uncertain. Here, we present the characterisation of three exceptionally distant LAEs at $z>8$, newly discovered by JWST/NIRSpec in the JADES survey. These three similarly bright ($M_\text{UV} \approx -20\,\mathrm{mag}$) LAEs exhibit small Ly$\mathrm{\alpha}$ velocity offsets from the systemic redshift, $\Delta v_\mathrm{Ly\alpha} \lesssim 200\,\mathrm{km\,s^{-1}}$, yet span a range of Ly$\mathrm{\alpha}$ equivalent widths ($15\,\AA$, $31\,\AA$, and $132\,\AA$). The former two show moderate Ly$\mathrm{\alpha}$ escape fractions ($f_\mathrm{esc,Ly\alpha} \approx 10\%$), whereas Ly$\mathrm{\alpha}$ escapes remarkably efficiently from the third ($f_\mathrm{esc,Ly\alpha} \approx 72\%$), which moreover is very compact (half-light radius of $90\pm10\,\mathrm{pc}$). We find these LAEs are low-mass galaxies dominated by very recent, vigorous bursts of star formation accompanied by strong nebular emission from metal-poor gas. We infer the two LAEs with modest $f_\mathrm{esc,Ly\alpha}$, one of which reveals evidence for ionisation by an active galactic nucleus, may have reasonably produced small ionised bubbles preventing complete IGM absorption of Ly$\mathrm{\alpha}$. The third, however, requires a $\sim 3\,\text{physical Mpc}$ bubble, indicating faint galaxies have contributed significantly. The most distant LAEs thus continue to be powerful observational probes into the earlier stages of reionisation., Comment: 25 pages, 13 figures, accepted for publication in MNRAS

The Near-infrared Spectrograph (NIRSpec) on the James Webb Space Telescope is uniquely suited to studying galaxies in the distant Universe with its combination of multi-object capabilities and sensitivity over a large range in wavelength (0.6-5.3 microns). Here we present the NIRSpec Wide survey, part of the NIRSpec Instrument Science Team's Guaranteed Time Observations, using NIRSpec's microshutter array to obtain spectra of more than 3200 galaxies at $z>1$ at both low- and high-resolution ($R\approx100$ and 2700) for a total of 105 hours. With 31 pointings covering $\approx$320 arcmin$^2$ across the five CANDELS fields with exquisite ancillary photometry from the Hubble Space Telescope, the NIRSpec Wide survey represents a fast and efficient way of using JWST to probe galaxies in the early Universe. Pointing centers are determined to maximize the observability of the rarest, high-value sources. Subsequently, the microshutter configurations are optimized to observe the maximum number of "census" galaxies with a selection function based primarily on HST/F160W magnitude, photometric/slitless grism redshift, and predicted \ha\ flux tracing the bulk of the galaxy population at cosmic noon ($z_{\rm med}=2.0$). We present details on the survey strategy, the target selection, an outline of the motivating science cases, and discuss upcoming public data releases to the community., Comment: Published in A&A. Data for pointings in AEGIS available for download at https://archive.stsci.edu/hlsp/wide (https://archive.stsci.edu/hlsps/wide/download_scripts/hlsp_wide_jwst_nirspec_all_multi_v1.0_spec-download.sh)

We present rest-frame optical data of the z~4 sub-millimeter galaxy GN20 obtained with JWST/NIRSpec in integral field spectroscopy (IFS) mode. The H$\alpha$ emission is asymmetric and clumpy and extends over a projected distance of more than 15 kpc. To first order, the large-scale ionised gas kinematics are consistent with a turbulent ($\sigma\sim90$ km/s), rotating disc ($v_{\rm rot}\sim500$ km/s), congruent with previous studies of its molecular and ionised gas kinematics. However, we also find clear evidence for non-circular motions in the H$\alpha$ kinematics. We discuss their possible connection with various scenarios, such as external perturbations, accretion or radial flows. In the centre of GN20, we find broad line emission (FWHM $\sim1000-2000$ km/s) in the H$\alpha$+[N II] complex, suggestive of fast, AGN-driven winds or, alternatively, of the broad-line region of an active black hole. Elevated values of [N II]$\lambda6583$/H$\alpha>0.4$ and EW(H$\alpha)>6$ \r{A}, throughout large parts of GN20 suggest that feedback from the active black hole is able to photo-ionise the interstellar medium. Our data corroborates that GN20 offers a unique opportunity to observe key processes in the evolution of the most massive present-day galaxies acting in concert, over 12 billion years ago., Comment: 12 pages, 8 figures; accepted for publication in MNRAS; doi:10.1093/mnras/stae1993

We present a study on stellar properties of Lyman-alpha (Ly$\alpha$) emitters at 5 $< z <$ 8.2. We use 247 photometrically-selected, lensed, high-redshift, low luminosity galaxy candidates with spectroscopic follow-up. Of these, 38 are confirmed spectroscopically to be between 5 $< z <$ 8.2 via detection of Ly$\alpha$. For each galaxy and candidate, we estimate stellar mass, star formation rate, specific star formation rate, and mass-weighted age with spectral energy distribution fitting. We also measure the UV $\beta$ slope and luminosity using values from photometry. We find no strong correlation between Ly$\alpha$ equivalent width and any of these properties, as well as no significant difference between the physical properties of Ly$\alpha$ emitters and candidates without Ly$\alpha$ detected. This lack of expected trends may be explained by a combination of the evolving opacity of the IGM at these redshifts as well as the unique phase space probed by our lensed sample. Via tests on other galaxy samples which show varying strengths of correlations, we conclude that if there exist any relationships between Ly$\alpha$ EW and physical properties in the underlying population of faint galaxies, they are weak correlations. We also present the results of a spectroscopic search for CIII] emission in confirmed Ly$\alpha$ emitters at $z \sim 7$, finding no CIII] detections, but putting constraints on strong AGN activity and extreme nebular emission., Comment: v2, 14 pages, 8 figures, accepted to MNRAS after minor updates

Extending earlier work of Guralnick and of Cai and Zhang, we classify the almost simple groups which have transitive permutation representations of prime power degree $p^k$, and those which have $p$-complements (stabilisers of order coprime to $p$ in such representations). We deduce that every primitive permutation group of prime power degree has a regular subgroup, and that any two faithful primitive representations of a group, of the same prime power degree, are equivalent under automorphisms. In general, $p$-complements in a finite group can be inequivalent under automorphisms, or even non-isomorphic. We extend examples of such phenomena due to Buturlakin, Revin and Nesterov by showing that the number of inequivalent classes of complements can be arbitrarily large. Questions concerning the existence of prime power representations and $p$-complements in groups with socle ${\rm PSL}_d(q)$ are related to some difficult open problems in Number Theory., Comment: 19 pages. We have added citations to related work of Kazarin and Nesterov, we have clarified the relationship of our work to theirs, and we have provided simpler proofs for some results in Section 6

Galaxy morphology is shaped by stellar activity, feedback, gas and dust properties, and interactions with surroundings, and can therefore provide insight into these processes. In this paper, we study the spatial offsets between stellar and interstellar medium emission in a sample of 54 main-sequence star-forming galaxies at $z\sim4-6$ observed with the Atacama Large Millimeter/submillimeter Array (ALMA) and drawn from the ALMA Large Program to INvestigate C$^+$ at Early times (ALPINE). We find no significant spatial offset for the majority ($\sim$ 70 percent) of galaxies in the sample among any combination of [C II], far-infrared continuum, optical, and ultraviolet emission. However, a fraction of the sample ($\sim$ 30 percent) shows offsets larger than the median by more than 3$\sigma$ significance (compared to the uncertainty on the offsets), especially between [C II] and ultraviolet emission. We find that these significant offsets are of the order of $\sim$0.5-0.7 arcsec, corresponding to $\sim$3.5-4.5 kiloparsecs. The offsets could be caused by a complex dust geometry, strong feedback from stars and active galactic nuclei, large-scale gas inflow and outflow, or a combination of these phenomena. However, our current analysis does not definitively constrain the origin. Future, higher resolution ALMA and JWST observations may help resolve the ambiguity. Regardless, since there exist at least some galaxies that display such large offsets, galaxy models and spectral energy distribution fitting codes cannot assume co-spatial emission in all main-sequence galaxies, and must take into account that the observed emission across wavelengths may be spatially segregated., Comment: 20 pages, 8 figures. Submitted to MNRAS; second revision

JWST has recently sparked a new era of Ly$\alpha$ spectroscopy, delivering the first measurements of the Ly$\alpha$ escape fraction and velocity profile in typical galaxies at $z\simeq6-10$. These observations offer new prospects for insight into the earliest stages of reionization. But to realize this potential, we need robust models of Ly$\alpha$ properties in galaxies at $z\simeq5-6$ when the IGM is mostly ionized. Here we use new JWST observations from the JADES and FRESCO surveys combined with VLT/MUSE and Keck/DEIMOS data to characterize statistical distributions of Ly$\alpha$ velocity offsets, escape fractions, and EWs in $z\simeq5-6$ galaxies. We find that galaxies with large Ly$\alpha$ escape fractions (> 0.2) are common at $z\simeq5-6$, comprising 30 per cent of Lyman break selected samples. Comparing to literature studies, our census suggests that Ly$\alpha$ becomes more prevalent in the galaxy population toward higher redshift from $z\sim3$ to $z\sim6$, although we find that this evolution slows considerably between $z\sim5$ and $z\sim6$, consistent with modest attenuation from residual HI in the mostly ionized IGM at $z\simeq5-6$. We find significant evolution in Ly$\alpha$ velocity profiles between $z\simeq2-3$ and $z\simeq5-6$, likely reflecting the influence of resonant scattering from residual intergalactic HI on the escape of Ly$\alpha$ emission near line center. This effect will make it challenging to use Ly$\alpha$ peak offsets as a probe of Lyman continuum leakage at $z\simeq5-6$. We use our $z\simeq5-6$ Ly$\alpha$ distributions to make predictions for typical Ly$\alpha$ properties at $z\gtrsim8$ and discuss implications of a recently-discovered Ly$\alpha$ emitter at $z\simeq8.5$ with a small peak velocity offset (156 km s$^{-1}$)., Comment: 31 pages, 12 figures, accepted by MNRAS

Extreme emission line galaxies (EELGs) exhibit large equivalent widths (EW) in their rest-optical emission lines ([OIII]$\lambda5007$ or H$\alpha$ rest-frame EW$ > 750\r{A}$) which can be tied to a recent upturn in star formation rate, due to the sensitivity of the nebular line emission and the rest-optical continuum to young ($<10$Myr) and evolved stellar populations, respectively. By studying a sample of 85 star forming galaxies (SFGs), spanning the redshift and magnitude interval $3 $ M$_{UV}>-21$, in the JWST Advanced Deep Extragalactic Survey (JADES) with NIRSpec/prism spectroscopy, we determine that SFGs initiate an EELG phase when entering a significant burst of star formation, with the highest EWs observed in EELGs with the youngest luminosity-weighted ages ($<5$ Myr old) and the highest burst intensity (those with the greatest excess between their current and long-term average SFR). We spectroscopically confirm that a greater proportion of SFGs are in an EELG phase at high redshift in our UV-selected sample ($61\pm4\%$ in our $z>5.7$ high-redshift bin, compared to $23^{+4}_{-1}\%$ in our lowest-redshift bin $35.7$ have observed Lyman-$\alpha$ emission, potentially lying within large ionised regions. The high detection rate of Lyman-$\alpha$ emitters in our EELG selection suggests that the physical conditions associated with entering an EELG phase also promote the escape of Lyman-$\alpha$ photons., Comment: 34 pages, 25 figures

Motivated by their research on automorphism groups of pseudo-real Riemann surfaces, Bujalance, Cirre and Conder have conjectured that there are infinitely many primes $p$ such that $p+2$ has all its prime factors $q\equiv -1$ mod~$(4)$. We use theorems of Landau and Raikov to prove that the number of integers $n\le x$ with only such prime factors $q$ is asymptotic to $cx/\sqrt{\ln x}$ for a specific constant $c=0.4865\ldots$. Heuristic arguments, following Hardy and Littlewood, then yield a conjecture that the number of such primes $p\le x$ is asymptotic to $c'\int_2^x(\ln t)^{-3/2}dt$ for a constant $c'=0.8981\ldots$. The theorem, the conjecture and a similar conjecture applying the Bateman--Horn Conjecture to other pseudo-real Riemann surfaces are supported by evidence from extensive computer searches., Comment: 20 pages

We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters spanning $0.4-0.9\mu\mathrm{m}$) and novel JWST images with 14 filters spanning $0.8-5\mu\mathrm{m}$, including 7 medium-band filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data at $>2.3\mu\mathrm{m}$ to construct an ultradeep image, reaching as deep as $\approx31.4$ AB mag in the stack and 30.3-31.0 AB mag ($5\sigma$, $r=0.1"$ circular aperture) in individual filters. We measure photometric redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts $z=11.5-15$. These objects show compact half-light radii of $R_{1/2}\sim50-200$pc, stellar masses of $M_{\star}\sim10^7-10^8 M_{\odot}$, and star-formation rates of $\mathrm{SFR}\sim0.1-1\,M_{\odot}\,\mathrm{yr}^{-1}$. Our search finds no candidates at $15

A surprising finding of recent studies is the large number of Active Galactic Nuclei (AGN) associated with moderately massive black holes ($\rm \log(M_\bullet/M_\odot)\sim 6-8$), in the first billion years after the Big Bang ($z>5$). In this context, a relevant finding has been the large fraction of candidate dual AGN, both at large separations (several kpc) and in close pairs (less than a kpc), likely in the process of merging. Frequent black hole merging may be a route for black hole growth in the early Universe; however, previous findings are still tentative and indirect. We present JWST/NIRSpec-IFU observations of a galaxy at $z=7.15$ in which we find evidence for a $\rm \log(M_\bullet/M_\odot)\sim7.7$ accreting black hole, as traced by a broad component of H$\beta$ emission, associated with the Broad Line Region (BLR) around the black hole. This BLR is offset by 620 pc in projection from the centroid of strong rest-frame optical emission, with a velocity offset of $\sim$40 km/s. The latter region is also characterized by (narrow) nebular emission features typical of AGN, hence also likely hosting another accreting black hole, although obscured (type 2, narrow-line AGN). We exclude that the offset BLR is associated with Supernovae or massive stars, and we interpret these results as two black holes in the process of merging. This finding may be relevant for estimates of the rate and properties of gravitational wave signals from the early Universe that will be detected by future observatories like LISA., Comment: 12 pages, 5 figures; accepted for publication in MNRAS; doi:10.1093/mnras/stae943

The SPT0311-58 system resides in a massive dark matter halo at z ~ 6.9. It hosts two dusty galaxies (E and W) with a combined star formation rate of ~3500 Msun/yr. Its surrounding field exhibits an overdensity of sub-mm sources, making it a candidate proto-cluster. We use spatially-resolved spectroscopy provided by the JWST/NIRSpec Integral Field Unit (IFU) to probe a field of view (FoV) ~ 17 x 17 kpc^2 around this object. These observations have revealed ten new galaxies at z ~ 6.9, characterised by dynamical masses spanning from ~10^9 to 10^10 Msun and a range in radial velocities of ~ 1500 km/s, in addition to the already known E and W galaxies. The implied large number density, and the wide spread in velocities, indicate that SPT0311-58 is at the core of a proto-cluster, immersed in a very massive dark matter halo of ~ 5 x 10^12 Msun. Hence, it represents the most massive proto-cluster ever found at the EoR. We also study the dynamical stage of the system and find that it likely is not fully virialised. The galaxies exhibit a great diversity of properties showing a range of evolutionary stages. We derive their ongoing Ha-based unobscured SFR, and find that its contribution to the total SF varies significantly across the galaxies in the system. Their ionization conditions range from those typical of field galaxies at similar redshift recently studied with JWST to those found in more evolved objects at lower z. The metallicity spans more than 0.8 dex across the FoV, reaching nearly solar values in some cases. The detailed IFU spectroscopy of the E galaxy reveals that it is actively assembling its stellar mass, showing sub-kpc inhomogeneities, and a metallicity gradient that can be explained by accretion of low metallicity gas from the IGM. The kinematic maps indicate departures from regular rotation, high turbulence, and a possible pre-collision minor merger. (Abridged), Comment: Revised version: minor changes, improved figures, updated references

We summarize the properties and initial data release of the JADES Origins Field (JOF), which will soon be the deepest imaging field yet observed with the James Webb Space Telescope (JWST). This field falls within the GOODS-S region about 8' south-west of the Hubble Ultra Deep Field (HUDF), where it was formed initially in Cycle 1 as a parallel field of HUDF spectroscopic observations within the JWST Advanced Deep Extragalactic Survey (JADES). This imaging will be greatly extended in Cycle 2 program 3215, which will observe the JOF for 5 days in six medium-band filters, seeking robust candidates for z>15 galaxies. This program will also include ultra-deep parallel NIRSpec spectroscopy (up to 104 hours on-source, summing over the dispersion modes) on the HUDF. Cycle 3 observations from program 4540 will add 20 hours of NIRCam slitless spectroscopy to the JOF. With these three campaigns, the JOF will be observed for 380 open-shutter hours with NIRCam using 15 imaging filters and 2 grism bandpasses. Further, parts of the JOF have deep 43 hr MIRI observations in F770W. Taken together, the JOF will soon be one of the most compelling deep fields available with JWST and a powerful window into the early Universe. This paper presents the second data release from JADES, featuring the imaging and catalogs from the year 1 JOF observations., Comment: Submitted to ApJ Supplement. Images and catalogs are available at https://archive.stsci.edu/hlsp/jades . A FITSmap portal to view the images is at https://jades.idies.jhu.edu

With the remarkable sensitivity and resolution of JWST in the infrared, measuring rest-optical kinematics of galaxies at $z>5$ has become possible for the first time. This study pilots a new method for measuring galaxy dynamics for highly multiplexed, unbiased samples by combining FRESCO NIRCam grism spectroscopy and JADES medium-band imaging. Here we present one of the first JWST kinematic measurements for a galaxy at $z>5$. We find a significant velocity gradient, which, if interpreted as rotation yields $V_{rot} = 240\pm50$km/s and we hence refer to this galaxy as Twister-z5. With a rest-frame optical effective radius of $r_e=2.25$kpc, the high rotation velocity in this galaxy is not due to a compact size as may be expected in the early universe but rather a high total mass, ${\rm log(M}_{dyn}/{\rm M}_\odot)=11.0\pm0.2$. This is a factor of roughly 4x higher than the stellar mass within the effective radius. We also observe that the radial H$\alpha$ equivalent width profile and the specific star formation rate map from resolved stellar population modeling is centrally depressed by a factor of $\sim1.5$ from the center to $r_e$. Combined with the morphology of the line-emitting gas in comparison to the continuum, this centrally suppressed star formation is consistent with a star-forming disk surrounding a bulge growing inside-out. While large, rapidly rotating disks are common to z~2, the existence of one after only 1Gyr of cosmic time, shown for the first time in ionized gas, adds to the growing evidence that some galaxies matured earlier than expected in the history of the universe., Comment: Fig. 3 shows the main result

Merger events can trigger gas accretion onto supermassive black holes (SMBHs) sitting at the centre of galaxies, and form close pairs of active galactic nuclei (AGN). The fraction of AGN in pairs gives key information to constrain the environmental properties and evolution of SMBHs and their host galaxies. However, the identification of dual AGN is difficult, and only very few have been found in the distant Universe so far. We report the serendipitous discovery of a triple AGN and four dual AGN (one considered as a candidate), with projected separations in the range 3-28 kpc. Their AGN classification is mostly based on classical optical emission line flux ratios, as observed with the Near-InfraRed Spectrograph (NIRSpec) on the James Webb Space Telescope (JWST), and is complemented with additional multi-wavelength diagnostics. The identification of these multiple AGN out of the 17 AGN systems in our GA-NIFS survey (i.e. ~ 20-30%), suggests that they might be more common than expected from the most recent cosmological simulations, which predict a fraction of dual AGN at least one order of magnitude smaller. This work highlights the exceptional capabilities of NIRSpec for detecting distant dual AGN, and prompts new investigations to better constrain their fraction across the cosmic time, and to inform upcoming cosmological simulations., Comment: 40 pages, 7 figures, submitted to Nature, comments welcome!

Dust-obscured galaxies are thought to represent an early evolutionary phase of massive galaxies in which the active galactic nucleus (AGN) is still deeply buried in significant amounts of dusty material and its emission is strongly suppressed. The unprecedented sensitivity of the James Webb Space Telescope enables us for the first time to detect the rest-frame optical emission of heavily obscured AGN and unveil the properties of the hidden accreting super-massive black holes (BHs). In this work, we present the JWST/NIRSpec IFS data of ALESS073.1, a massive, dusty, star-forming galaxy at $z = 4.76$ hosting an AGN at its center. The detection of a very broad $H_\alpha$ emission associated with the Broad Line Region (BLR) confirms the presence of a BH ($\log(M_{BH}/M_\odot)>8.7$) accreting at less than 15\% of its Eddington limit and classifies the target as a Type 1 AGN. The rest-frame optical emission lines also reveal a fast ionized gas outflow marginally resolved in the galaxy center. The high sensitivity of NIRSpec allows us to perform the kinematic analysis of the narrow H$\alpha$ component which indicates that the warm ionized gas velocity field is consistent with disk rotation. We also find that, in the innermost nuclear regions ($< 1.5$ kpc), the intrinsic velocity dispersion of the disk reaches $\sim 150$ km/s, $\sim 2-3$ times higher than the velocity dispersion inferred from the [CII] 158$\mu$m line tracing mostly cold gas. Since, at large radii, the velocity dispersion of the warm and cold gas are comparable, we conclude that the outflows are injecting turbulence in the warm ionized gas in the central region, but they are not sufficiently powerful to disrupt the dense gas and quench star formation. These findings support the scenario that dust-obscured galaxies represent the evolutionary stage preceding the unobscured quasar when all gas and dust are removed from the host., Comment: 16 pages, 12 figures, accepted in A&A

We explore the kinematic gas properties of six $5.51$ thus far. The cold gas masses implied by the observed star formation rates are $\sim 10\times$ larger than the stellar masses. We find that their ionised gas is spatially resolved by JWST, with evidence for broadened lines and spatial velocity gradients. Using a simple thin-disc model, we fit these data with a novel forward modelling software that accounts for the complex geometry, point spread function, and pixellation of the NIRSpec instrument. We find the sample to include both rotation- and dispersion-dominated structures, as we detect velocity gradients of $v(r_{\rm e})\approx100-150\,{\rm km\,s^{-1}}$, and find velocity dispersions of $\sigma_0\approx 30-70\,{\rm km\,s^{-1}}$ that are comparable to those at cosmic noon. The dynamical masses implied by these models ($M_{\rm dyn}\sim10^{9-10}\,{\rm M_\odot}$) are larger than the stellar masses by up to a factor 40, and larger than the total baryonic mass (gas + stars) by a factor of $\sim 3$. Qualitatively, this result is robust even if the observed velocity gradients reflect ongoing mergers rather than rotating discs. Unless the observed emission line kinematics is dominated by outflows, this implies that the centres of these galaxies are dark-matter dominated or that star formation is $3\times$ less efficient, leading to higher inferred gas masses., Comment: Accepted for publication in A&A. Software for JWST/NIRSpec MSA modelling (slit losses, 1D LSFs and 2D model fitting) publicly available at https://github.com/annadeg/jwst-msafit

There is compelling evidence that the most massive galaxies in the Universe stopped forming stars due to the time-integrated feedback from their central super-massive black holes (SMBHs). However, the exact quenching mechanism is not yet understood, because local massive galaxies were quenched billions of years ago. We present JWST/NIRSpec integral-field spectroscopy observations of GS-10578, a massive, quiescent galaxy at redshift z=3.064. From the spectrum we infer that the galaxy has a stellar mass of $M_*=1.6\pm0.2 \times 10^{11}$ MSun and a dynamical mass $M_{\rm dyn}=2.0\pm0.5 \times 10^{11}$ MSun. Half of its stellar mass formed at z=3.7-4.6, and the system is now quiescent, with the current star-formation rate SFR<9 MSun/yr. We detect ionised- and neutral-gas outflows traced by [OIII] emission and NaI absorption. Outflow velocities reach $v_{\rm out}\approx$1,000 km/s, comparable to the galaxy escape velocity and too high to be explained by star formation alone. GS-10578 hosts an Active Galactic Nucleus (AGN), evidence that these outflows are due to SMBH feedback. The outflow rates are 0.14-2.9 and 30-300 MSun/yr for the ionised and neutral phases, respectively. The neutral outflow rate is ten times higher than the SFR, hence this is direct evidence for ejective SMBH feedback, with mass-loading capable of interrupting star formation by rapidly removing its fuel. Stellar kinematics show ordered rotation, with spin parameter $\lambda_{Re}=0.62\pm0.07$, meaning GS-10578 is rotation supported. This study shows direct evidence for ejective AGN feedback in a massive, recently quenched galaxy, thus clarifying how SMBHs quench their hosts. Quenching can occur without destroying the stellar disc., Comment: 40 pages, 9 figures, submitted to Nat. Ast., comments welcome!

We present 12 new AGN at 4 10^44 erg/s, among galaxies in the redshift range 4 10%., Comment: Accepted for publication in A&A. 26 pages, 13 figures, 4 tables. Replaced with the accepted version (minor changes)

We characterize the physical properties of star-formation driven outflows in a sample of 29 local dwarf galaxies drawn from the Dwarf Galaxy Survey. We make use of Herschel/PACS archival data to search for atomic outflow signatures in the wings of individual [CII] 158 um spectra and in their stacked line profile. We find a clear excess of emission in the high-velocity tails of 11 sources which can be explained with an additional broad component in the modeling of their spectra. The remaining objects are likely hosts of weaker outflows that can still be detected in the average stacked spectrum. In both cases, we estimate the atomic mass outflow rates which result to be comparable with the star-formation rates of the galaxies, implying mass-loading factors of the order of unity. Outflow velocities in all the 11 galaxies with individual detection are larger than (or compatible with) the escape velocities of their dark matter halos, with an average fraction of 40% of gas escaping into the intergalactic medium (IGM). Depletion timescales due to outflows are lower than those due to gas consumption by star formation in most of our sources, ranging from hundred million to a few billion years. Our outflows are mostly consistent with momentum-driven winds generated by the radiation pressure of young stellar populations on dust grains, although the energy-driven scenario is not excluded if considering a coupling efficiency up to 20% between the energy injected by supernova (SN) and the interstellar medium. Our results suggest that galactic outflows can regulate the star formation history of dwarf galaxies as they are able to enrich with metals the circumgalactic medium of these sources, bringing on average a non-negligible amount of gas into the IGM. Our findings are suitable for tuning chemical evolution models attempting to describe the physical processes shaping the evolution of dwarf galaxies., Comment: Accepted for publication in A&A

We present a study of the environments of 17 Lyman-$\alpha$ (Ly$\alpha$) emitting galaxies (LAEs) in the reionisation era ($5.8 < z < 8$) identified by JWST/NIRSpec as part of the JWST Advanced Deep Extragalactic Survey (JADES). Unless situated in sufficiently (re)ionised regions, Ly$\alpha$ emission from these galaxies would be strongly absorbed by neutral gas in the intergalactic medium (IGM). We conservatively estimate sizes of the ionised regions required to reconcile the relatively low Ly$\alpha$ velocity offsets ($\Delta v_\text{Ly$\alpha$}<300\,\mathrm{km\,s^{-1}}$) with moderately high Ly$\alpha$ escape fractions ($f_\mathrm{esc,\,Ly\alpha}>5\%$) observed in our sample of LAEs, suggesting the presence of ionised hydrogen along the line of sight towards at least eight out of 17 LAEs. We find minimum physical `bubble' sizes of the order of $R_\text{ion}\sim0.1$-$1\,\mathrm{pMpc}$ are required in a patchy reionisation scenario where ionised bubbles containing the LAEs are embedded in a fully neutral IGM. Around half of the LAEs in our sample are found to coincide with large-scale galaxy overdensities seen in FRESCO at $z \sim 5.8$-$5.9$ and $z\sim7.3$, suggesting Ly$\alpha$ transmission is strongly enhanced in such overdense regions, and underlining the importance of LAEs as tracers of the first large-scale ionised bubbles. Considering only spectroscopically confirmed galaxies, we find our sample of UV-faint LAEs ($M_\text{UV}\gtrsim-20\,\mathrm{mag}$) and their direct neighbours are generally not able to produce the required ionised regions based on the Ly$\alpha$ transmission properties, suggesting lower-luminosity sources likely play an important role in carving out these bubbles. These observations demonstrate the combined power of JWST multi-object and slitless spectroscopy in acquiring a unique view of the early Universe during cosmic reionisation via the most distant LAEs., Comment: 15 pages, 8 figures. Accepted for publication in A&A