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The use of Gaussian Process Regression (GPR) for foregrounds mitigation in data collected by the LOw-Frequency ARray (LOFAR) to measure the high-redshift 21-cm signal power spectrum has been shown to have issues of signal loss when the 21-cm signal covariance is misestimated. To address this problem, we have recently introduced covariance kernels obtained by using a Machine Learning based Variational Auto-Encoder (VAE) algorithm in combination with simulations of the 21-cm signal. In this work, we apply this framework to 141 hours ($\approx 10$ nights) of LOFAR data at $z \approx 9.1$, and report revised upper limits of the 21-cm signal power spectrum. Overall, we agree with past results reporting a 2-$\sigma$ upper limit of $\Delta^2_{21} < (80)^2~\rm mK^2$ at $k = 0.075~h~\rm Mpc^{-1}$. Further, the VAE-based kernel has a smaller correlation with the systematic excess noise, and the overall GPR-based approach is shown to be a good model for the data. Assuming an accurate bias correction for the excess noise, we report a 2-$\sigma$ upper limit of $\Delta^2_{21} < (25)^2~\rm mK^2$ at $k = 0.075~h~\rm Mpc^{-1}$. However, we still caution to take the more conservative approach to jointly report the upper limits of the excess noise and the 21-cm signal components., Comment: 5 pages, 3 figures, 2 tables. Accepted for publication in the Monthly Notices of the Royal Astronomical Society (MNRAS) Letters

The high redshift 21-cm signal promises to be a crucial probe of the state of the intergalactic medium (IGM). Understanding the connection between the observed 21-cm power spectrum and the physical quantities intricately associated with the IGM is crucial to fully understand the evolution of our Universe. In this study, we develop an emulator using artificial neural network (ANN) to predict the 21-cm power spectrum from a given set of IGM properties, namely, the bubble size distribution and the volume averaged ionization fraction. This emulator is implemented within a standard Bayesian framework to constrain the IGM parameters from a given 21-cm power spectrum. We compare the performance of the Bayesian method to an alternate method using ANN to predict the IGM parameters from a given input power spectrum, and find that both methods yield similar levels of accuracy, while the ANN is significantly faster. We also use this ANN method of parameter estimation to predict the IGM parameters from a test set contaminated with noise levels expected from the SKA-LOW instrument after 1000 hours of observation. Finally, we train a separate ANN to predict the source parameters from the IGM parameters directly, at a redshift of $z=9.1$, demonstrating the possibility of a non-analytic inference of the source parameters from the IGM parameters for the first time. We achieve high accuracies, with R2-scores ranging between $0.898-0.978$ for the ANN emulator and between $0.966-0.986$ and $0.817-0.981$ for the predictions of IGM parameters from 21-cm power spectrum and source parameters from IGM parameters, respectively. The predictions of the IGM parameters from the Bayesian method incorporating the ANN emulator leads to tight constraints with error bars around $\pm{0.14}$ on the IGM parameters.

A rather clear problem has remained in black hole physics: localizing black holes. One of the recent theoretical ways proposed to identify black hole mergers' hosts is through multi-messenger gravitational lensing: matching the properties of a lensed galactic host with those of a lensed gravitational wave. This paper reviews the most recent literature and introduces some of the ongoing work on the localization of binary black holes and their host galaxies through lensing of gravitational waves and their electromagnetically-bright hosts., Comment: 17 pages, 4 figures. Proceedings from the Royal Society Meeting for Multi-messenger Lensing (2024). Submitted to Phil. Trans. A

The redshifted 21-cm signal from the epoch of reionization (EoR) directly probes the ionization and thermal states of the intergalactic medium during that period. In particular, the distribution of the ionized regions around the radiating sources during EoR introduces scale-dependent features in the spherically-averaged EoR 21-cm signal power spectrum. The goal is to study these scale-dependent features at different stages of reionization using numerical simulations and build a source model-independent framework to probe the properties of the intergalactic medium using EoR 21-cm signal power spectrum measurements. Under the assumption of high spin temperature, we modelled the redshift evolution of the ratio of EoR 21-cm brightness temperature power spectrum and the corresponding density power spectrum using an ansatz consisting of a set of redshift and scale-independent parameters. This set of eight parameters probes the redshift evolution of the average ionization fraction and the quantities related to the morphology of the ionized regions. We have tested this ansatz on different reionization scenarios generated using different simulation algorithms and found that it is able to recover the redshift evolution of the average neutral fraction within an absolute deviation $\lesssim 0.1$. Our framework allows us to interpret 21-cm signal power spectra in terms of parameters related to the state of the IGM. This source model-independent framework can efficiently constrain reionization scenarios using multi-redshift power spectrum measurements with ongoing and future radio telescopes such as LOFAR, MWA, HERA, and SKA. This will add independent information regarding the EoR IGM properties., Comment: 16 pages, 13 figures, 2 tables, Accepted for publication in Astronomy and Astrophysics

Convolutional neural networks (CNNs) are the state-of-the-art technique for identifying strong gravitational lenses. Although they are highly successful in recovering genuine lens systems with a high true-positive rate, the unbalanced nature of the data set (lens systems are rare), still leads to a high false positive rate. For these techniques to be successful in upcoming surveys (e.g. with Euclid) most emphasis should be set on reducing false positives, rather than on reducing false negatives. In this paper, we introduce densely connected neural networks (DenseNets) as the CNN architecture in a new pipeline-ensemble model containing an ensemble of classification CNNs and regression CNNs to classify and rank-order lenses, respectively. We show that DenseNets achieve comparable true positive rates but considerably lower false positive rates (when compared to residual networks; ResNets). Thus, we recommend DenseNets for future missions involving large data sets, such as Euclid, where low false positive rates play a key role in the automated follow-up and analysis of large numbers of strong gravitational lens candidates when human vetting is no longer feasible

During the early stages of galaxy evolution, a significant fraction of galaxies undergo a transitional phase between the ``blue nugget" systems, which arise from the compaction of large, active star-forming disks, and the ``red nuggets", which are red and passive compact galaxies. These objects are typically only observable with space telescopes, and detailed studies of their size, mass, and stellar population parameters have been conducted on relatively small samples. Strong gravitational lensing can offer a new opportunity to study them in detail, even with ground-based observations. In this study, we present the first 6 \textit{bona fide} sample of strongly lensed post-blue nugget (pBN) galaxies, which were discovered in the Kilo Degree Survey. By using the lensing-magnified luminosity from optical and near-infrared bands, we have derived robust structural and stellar population properties of the multiple images of the background sources. \rui{The pBN galaxies have very small sizes of $\rm R_{eff}<1.3$ kpc, high mass density inside 1 kpc of $ \rm \log (\Sigma_1/M_{\odot} \mathrm{kpc}^{-2})>9.3$, and low specific star formation rates of $\log (\mathrm{sSFR/Gyr})\lesssim0$, The size-mass and $\Sigma_1$-mass relations of this sample are consistent with those of the red nuggets, while their sSFR is close to the lower end of compact star-forming blue nugget systems at the same redshift, suggesting a clear evolutionary link between them., Comment: Accepted for publication in APJ

We compare the structural properties and dark matter content of star-forming galaxies taken from the CAMELS cosmological simulations to the observed trends derived from the SPARC sample in the stellar mass range $[10^{9}, 10^{11}]\,\textrm{M}_{\odot}$, to provide constraints on the value of cosmological and astrophysical (SN- and AGN-related) parameters. We consider the size-, internal DM fraction-, internal DM mass- and total-stellar mass relations for all the 1065 simulations from the IllustrisTNG, SIMBA and ASTRID suites of CAMELS, and search for the parameters that minimize the $\chi^{2}$ with respect to the observations. For the IllustrisTNG suite, we find the following constraints for the cosmological parameters: $\Omega_{\textrm{m}} = 0.27_{-0.05}^{+0.01}$, $\sigma_{8} = 0.83_{-0.11}^{+0.08}$ and $S_{8} = 0.78_{-0.09}^{+0.03}$, which are consistent within $1\sigma$ with the results from the nine-year WMAP observations. SN feedback-related astrophysical parameters, which describe the departure of outflow wind energy per unit star formation rate and wind velocity from the reference IllustrisTNG simulations, assume the following values: $A_{\textrm{SN1}} = 0.48_{-0.16}^{+0.25}$ and $A_{\textrm{SN2}} = 1.21_{-0.34}^{+0.03}$, respectively. Therefore, simulations with a lower value of outflow wind energy per unit star formation rate with respect to the reference illustrisTNG simulation better reproduce the observations. Simulations based on SIMBA and ASTRID suites predict central dark matter masses substantially larger than those observed in real galaxies, which can be reconciled with observations only by requiring values of $\Omega_{\textrm{m}}$ inconsistent with cosmological constraints for SIMBA, or simulations characterized by unrealistic galaxy mass distributions for ASTRID., Comment: 24 pages, 10 figures, 9 tables. Accepted by MNRAS for publication; Added a reference to sec. 4.1

Inspired by the discussion in the community on possible hidden systematic errors in late universe cosmological probes and non-trivial physical models developed to reduce the Hubble tension, we investigate the Pantheon and Pantheon+ SNe samples for possible deviations from the original $\Lambda$CDM analysis. To simultaneously account for possible systematics or deviations from $\Lambda$CDM, we adopt Gaussian processes to model additional covariance while making no further assumptions on their origin. We explore both stationary and non-stationarity corrections to the covariance. While small changes in the inferred cosmological parameters $H_0$ and $\Omega_{m}$ can occur, we find no statistically significant evidence for missing covariance. We find an upper limit for the Gaussian processes amplitude $\sigma < 0.031$ mag with $95\%$ confidence, which corresponds to $20\%$ of the average statistical error in the Pantheon+ sample. The strongest effect we find on the inferred cosmological parameter posterior can reduce the statistical significance of the Hubble tension between Pantheon+ and Planck estimates from 5.3$\sigma$ to 4.5$\sigma$. Therefore, we conclude that the SN cosmological parameter inference is robust against the analysis modifications studied in this work., Comment: 16 pages, 6 figures, prepared for submission to JCAP

To self-consistently model galactic properties, reionization of the intergalactic medium, and the associated 21-cm signal, we have developed the algorithm polar by integrating the one-dimensional radiative transfer code grizzly with the semi-analytical galaxy formation code L-Galaxies 2020. Our proof-of-concept results are consistent with observations of the star formation rate history, UV luminosity function and the CMB Thomson scattering optical depth. We then investigate how different galaxy formation models affect UV luminosity functions and 21-cm power spectra, and find that while the former are most sensitive to the parameters describing the merger of halos, the latter have a stronger dependence on the supernovae feedback parameters, and both are affected by the escape fraction model., Comment: MNRAS accepted

Wave-mechanical effects in gravitational lensing have long been predicted, and with the discovery of populations of compact transients such as gravitational wave events and fast radio bursts, may soon be observed. We present an observer's review of the relevant theory underlying wave-mechanical effects in gravitational lensing. Starting from the curved-spacetime scalar wave equation, we derive the Fresnel-Kirchoff diffraction integral, and analyze it in the eikonal and wave optics regimes. We answer the question of what makes interference effects observable in some systems but not in others, and how interference effects allow for complementary information to be extracted from lensing systems as compared to traditional measurements. We end by discussing how diffraction effects affect optical depth forecasts and lensing near caustics, and how compact, low-frequency transients like gravitational waves and fast radio bursts provide promising paths to open up the frontier of interferometric gravitational lensing., Comment: Comments and suggestions for additional references welcome

Interstellar scattering (ISS) of radio pulsar emission can be used as a probe of the ionised interstellar medium (IISM) and causes corruptions in pulsar timing experiments. Two types of ISS phenomena (intensity scintillation and pulse broadening) are caused by electron density fluctuations on small scales (< 0.01 AU). Theory predicts that these are related, and both have been widely employed to study the properties of the IISM. Larger scales ($\sim$1-100\,AU) cause measurable changes in dispersion and these can be correlated with ISS observations to estimate the fluctuation spectrum over a very wide scale range. IISM measurements can often be modeled by a homogeneous power-law spatial spectrum of electron density with the Kolmogorov ($-11/3$) spectral exponent. Here we aim to test the validity of using the Kolmogorov exponent with PSR~J0826+2637. We do so using observations of intensity scintillation, pulse broadening and dispersion variations across a wide fractional bandwidth (20 -- 180\,MHz). We present that the frequency dependence of the intensity scintillation in the high frequency band matches the expectations of a Kolmogorov spectral exponent but the pulse broadening in the low frequency band does not change as rapidly as predicted with this assumption. We show that this behavior is due to an inhomogeneity in the scattering region, specifically that the scattering is dominated by a region of transverse size $\sim$40\,AU. The power spectrum of the electron density, however, maintains the Kolmogorov spectral exponent from spatial scales of 5$\times10^{-6}$\,AU to $\sim$100\,AU., Comment: Accepted for publication in MNRAS, typo fixed

The light-cone (LC) anisotropy arises due to cosmic evolution of the cosmic dawn 21-cm signal along the line-of-sight (LoS) axis of the observation volume. The LC effect makes the signal statistically non-ergodic along the LoS axis. The multi-frequency angular power spectrum (MAPS) provides an unbiased alternative to the popular 3D power spectrum as it does not assume statistical ergodicity along every direction in the signal volume. Unlike the 3D power spectrum which mixes the cosmic evolution of the 21-cm signal along the LoS $k$ modes, MAPS keeps the evolution information disentangled. Here we first study the impact of different underlying physical processes during cosmic dawn on the behaviour of the 21-cm MAPS using simulations of various different scenarios and models. We also make error predictions in 21-cm MAPS measurements considering only the system noise and cosmic variance for mock observations of HERA, NenuFAR and SKA-Low. We find that $100~{\rm h}$ of HERA observations will be able to measure 21-cm MAPS at $\geq 3\sigma$ for $\ell \lesssim 1000$ with $0.1\,{\rm MHz}$ channel-width. The better sensitivity of SKA-Low allows reaching this sensitivity up to $\ell \lesssim 3000$. Note that due to the difference in the frequency coverage of the various experiements, the CD-EoR model considered for NenuFAR is different than those used for the HERA and SKA-Low predictions. Considering NenuFAR with the new model, measurements $\geq 2\sigma$ are possible only for $\ell \lesssim 600$ with $0.2\,{\rm MHz}$ channel-width and for a ten times longer observation time of $t_{\rm obs} = 1000~{\rm h}$. However, for the range $300 \lesssim \ell \lesssim 600$ and $t_{\rm obs}=1000~{\rm h}$ more than $3\sigma$ measurements are still possible for NenuFAR when combining consecutive frequency channels within a $5 ~{\rm MHz}$ band., Comment: 21 pages, 12 figures, 3 tables, accepted for publication in MNRAS

The measurement of the $21$ cm signal from the Cosmic Dawn is a major goal for several existing and upcoming radio interferometers such as NenuFAR and the SKA. During this era before the beginning of the Epoch of Reionization, the signal is more difficult to observe due to brighter foregrounds but reveals additional information on the underlying astrophysical processes encoded in the spatial fluctuations of the spin temperature of hydrogen. To interpret future measurements, controlling the level of accuracy of the Lyman-$\alpha$ flux modelling is mandatory. In this work, we evaluate the impact of various approximations that exist in the main fast modelling approach compared to the results of a costly full radiative transfer simulation. The fast SPINTER code, presented in this work, computes the Lyman-$\alpha$ flux including the effect of wing scatterings for an inhomogeneous emissivity field, but assuming an otherwise homogeneous expanding universe. The LICORICE code computes the full radiative transfer in the Lyman-$\alpha$ line without any substantial approximation. We find that the difference between homogeneous and inhomogeneous gas density and temperature is very small for the computed flux. On the contrary, neglecting the effect of gas velocities produces a significant change in the computed flux. We identify the causes (mainly Doppler shifts due to velocity gradients) and quantify the magnitude of the effect in both an idealised setup and a realistic cosmological situation. We find that the amplitude of the effect, up to a factor of $\sim 2$ on the $21$ cm signal power spectrum on some scales (depending on both other model parameters and the redshift), can be easily discriminated with an SKA-like survey and already be approached, particularly for exotic signals, by the ongoing NenuFAR Cosmic Dawn Key Science Program., Comment: 14 pages, accepted for publication in A&A

In a sky-averaged 21-cm signal experiment, the uncertainty on the extracted signal depends mainly on the covariance between the foreground and 21-cm signal models. In this paper, we construct these models using the modes of variation obtained from the Singular Value Decomposition of a set of simulated foreground and 21-cm signals. We present a strategy to reduce this overlap between the 21-cm and foreground modes by simultaneously fitting the spectra from multiple different antennas, which can be used in combination with the method of utilizing the time dependence of foregrounds while fitting multiple drift scan spectra. To demonstrate this idea, we consider two different foreground models (i) a simple foreground model, where we assume a constant spectral index over the sky, and (ii) a more realistic foreground model, with a spatial variation of the spectral index. For the simple foreground model, with just a single antenna design, we are able to extract the signal with good accuracy if we simultaneously fit the data from multiple time slices. The 21-cm signal extraction is further improved when we simultaneously fit the data from different antennas as well. This improvement becomes more pronounced while using the more realistic mock observations generated from the detailed foreground model. We find that even if we fit multiple time slices, the recovered signal is biased and inaccurate for a single antenna. However, simultaneously fitting the data from different antennas reduces the bias and the uncertainty by a factor of 2-3 on the extracted 21-cm signal., Comment: 12 pages, 13 figures. Accepted for publication in MNRAS. Accompanying code is available https://github.com/anchal-009/SAVED21cm

The unprecedented number of gravitational lenses expected from new-generation facilities such as the ESA Euclid telescope and the Vera Rubin Observatory makes it crucial to rethink our classical approach to lens-modelling. In this paper, we present LeMoN (Lens Modelling with Neural networks): a new machine-learning algorithm able to analyse hundreds of thousands of gravitational lenses in a reasonable amount of time. The algorithm is based on a Bayesian Neural Network: a new generation of neural networks able to associate a reliable confidence interval to each predicted parameter. We train the algorithm to predict the three main parameters of the Singular Isothermal Ellipsoid model (the Einstein radius and the two components of the ellipticity) by employing two simulated datasets built to resemble the imaging capabilities of the Hubble Space Telescope and the forthcoming Euclid satellite. In this work, we assess the accuracy of the algorithm and the reliability of the estimated uncertainties by applying the network to several simulated datasets of 10.000 images each. We obtain accuracies comparable to previous studies present in the current literature and an average modelling time of just 0.5s per lens. Finally, we apply the LeMoN algorithm to a pilot dataset of real lenses observed with HST during the SLACS program, obtaining unbiased estimates of their SIE parameters. The code is publicly available on GitHub (https://github.com/fab-gentile/LeMoN)., Comment: Submitted to MNRAS; The code will be available on GitHub upon acceptance of the paper

One of the various versions of the classical Lyapunov-Poincar\'e center theorem states that a nondegenerate real analytic center type planar vector field singularity admits an analytic first integral. In a more proof of this result, R. Moussu establishes important connection between this result and the theory of singularities of holomorphic foliations (\cite{moussu}). In this paper we consider generalizations for two main frameworks: (i) planar real analytic vector fields with "many" periodic orbits near the singularity and (ii) germs of holomorphic foliations having a suitable singularity in dimension two. In this paper we prove versions of Poincar\'e-Lyapunov center theorem, including for the case of holomorphic vector fields. We also give some applications, hinting that there is much more to be explored in this framework., Comment: arXiv admin note: substantial text overlap with arXiv:2007.05414

To unlock the full spectrum of astrophysical and cosmological applications of gravitational-wave detections, it is essential to localise the associated black-hole mergers to high precision inside their host galaxies. One possible method to achieve this is to compare the properties of multiple detections of gravitationally-lensed binary black-hole merger events with the properties of strong gravitational lens systems located in the joint sky localisation of the gravitational-wave detections. In this work, we simulate the population of binary black-hole mergers lensed by galaxy-scale lenses and detectable by LIGO-Virgo-Kagra in the coming decade and the population of galaxy-scale strong lenses that will be detected by Euclid. We use these simulations to investigate the prospects for localising strongly lensed binary black-hole mergers inside the lensed galaxies of 'Euclid-like' galaxy-scale strong lenses. We find that for 20-50% of strongly lensed gravitational wave events the lens system is detectable with Euclid, if the event falls in its survey footprint. Of these, we expect to correctly identify the strongly-lensed host galaxy as likely (with posterior probability) host galaxy - based on Bayesian evidence ranking of candidate hosts - for 34.6-21.9% of quadruply-lensed gravitational-wave events when given an a-priori 1-5 deg^2 gravitational-wave-only sky localisation. For triply and doubly lensed gravitational-wave events, this becomes 29.8-14.9% and 16.4-6.6% respectively. If successfully identified, however, the localisation can be better than a fraction of the host-galaxy size, i.e. of order milli-arcseconds. A first detection in the coming decade, however, probably requires dedicated deep and high-resolution follow-ups and continued upgrades in the current and planned gravitational-wave detectors., Comment: 23 pages, 14 figures, 3 tables. Accepted for publication in MNRAS

In this paper we will list a few important goals that need to be addressed in the next decade, also taking into account the current discordances between the different cosmological probes, such as the disagreement in the value of the Hubble constant $H_0$, the $\sigma_8$--$S_8$ tension, and other less statistically significant anomalies. While these discordances can still be in part the result of systematic errors, their persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the necessity for new physics or generalisations beyond the standard model. In this paper, we focus on the $5.0\,\sigma$ tension between the {\it Planck} CMB estimate of the Hubble constant $H_0$ and the SH0ES collaboration measurements. After showing the $H_0$ evaluations made from different teams using different methods and geometric calibrations, we list a few interesting new physics models that could alleviate this tension and discuss how the next decade's experiments will be crucial. Moreover, we focus on the tension of the {\it Planck} CMB data with weak lensing measurements and redshift surveys, about the value of the matter energy density $\Omega_m$, and the amplitude or rate of the growth of structure ($\sigma_8,f\sigma_8$). We list a few interesting models proposed for alleviating this tension, and we discuss the importance of trying to fit a full array of data with a single model and not just one parameter at a time. Additionally, we present a wide range of other less discussed anomalies at a statistical significance level lower than the $H_0$--$S_8$ tensions which may also constitute hints towards new physics, and we discuss possible generic theoretical approaches that can collectively explain the non-standard nature of these signals.[Abridged], Comment: Contribution to Snowmass 2021. 224 pages, 27 figures. Accepted for publication in JHEAp

Forthcoming large imaging surveys such as Euclid and the Vera Rubin Observatory Legacy Survey of Space and Time are expected to find more than $10^5$ strong gravitational lens systems, including many rare and exotic populations such as compound lenses, but these $10^5$ systems will be interspersed among much larger catalogues of $\sim10^9$ galaxies. This volume of data is too much for visual inspection by volunteers alone to be feasible and gravitational lenses will only appear in a small fraction of these data which could cause a large amount of false positives. Machine learning is the obvious alternative but the algorithms' internal workings are not obviously interpretable, so their selection functions are opaque and it is not clear whether they would select against important rare populations. We design, build, and train several Convolutional Neural Networks (CNNs) to identify strong gravitational lenses using VIS, Y, J, and H bands of simulated data, with F1 scores between 0.83 and 0.91 on 100,000 test set images. We demonstrate for the first time that such CNNs do not select against compound lenses, obtaining recall scores as high as 76\% for compound arcs and 52\% for double rings. We verify this performance using Hubble Space Telescope (HST) and Hyper Suprime-Cam (HSC) data of all known compound lens systems. Finally, we explore for the first time the interpretability of these CNNs using Deep Dream, Guided Grad-CAM, and by exploring the kernels of the convolutional layers, to illuminate why CNNs succeed in compound lens selection., Comment: MNRAS accepted. 16 pages, 17 figures, The code used in this paper is publicly available at github.com/JoshWilde/LensFindery-McLensFinderFace

Reconstructing lens potentials and lensed sources can easily become an underconstrained problem, even when the degrees of freedom are low, due to degeneracies, particularly when potential perturbations superimposed on a smooth lens are included. Regularization has traditionally been used to constrain the solutions where the data failed to do so, e.g. in unlensed parts of the source. In this exploratory work, we go beyond the usual choices of regularization and adopt observationally motivated priors for the source brightness. We also perform a similar comparison when reconstructing lens potential perturbations, which are assumed to be stationary, i.e. permeate the entire field of view. We find that physically motivated priors lead to lower residuals, avoid overfitting, and are decisively preferred within a Bayesian quantitative framework in all the examples considered. For the perturbations, choosing the wrong regularization can have a detrimental effect that even high-quality data cannot correct for, while using a purely smooth lens model can absorb them to a very high degree and lead to biased solutions. Finally, our new implementation of the semi-linear inversion technique provides the first quantitative framework for measuring degeneracies between the source and the potential perturbations., Comment: 25 pages, 21 figures, 5 tables, submitted to MNRAS

We investigate tomography of 21-cm brightness temperature fluctuations during the Dark Ages as a probe for constraining primordial non-Gaussianity. We expand the 21- cm brightness temperature up to cubic order in perturbation theory and improve previous models of the signal by including the effect of the free electron fraction. Using modified standard perturbation theory methods that include baryonic pressure effects we derive an improved secondary bispectrum and for the first time derive the secondary trispectrum of 21-cm brightness temperature fluctuations. We then forecast the amount of information available from the Dark Ages to constrain primordial non-Gaussianity, including the imprints of massive particle exchange during inflation and we determine how much signal is lost due to secondary non-Gaussianity. We find that although secondary non-Gaussianity swamps the primordial signal, primordial non-Gaussianity can still be extracted with signal-to-noise ratios that surpass current and future CMB experiments by several orders of magnitude, depending on the experimental setup. Furthermore, we conclude that for the bi- and trispectra of massive particle exchange marginalizing over other primordial shapes affects signal-to-noise ratios more severely than secondary shapes. Baryonic pressure effects turn out to have a negligible impact on our forecasts, even at scales close to the Jeans scale. The results of this work reinforce the prospects of 21-cm brightness temperature fluctuations from the Dark Ages as the ultimate probe for primordial non-Gaussianity., Comment: 47 pages, 20 figures, code available at https://github.com/tsfloss/21-cm-Dark-Ages-Fisher-Forecast. v2: minor typos corrected. v3: matches published version

NenuFAR, the New Extension in Nancay Upgrading LOFAR, is currently in its early science phase. It is in this context that the Cosmic Filaments and Magnetism Pilot Survey is observing sources with the array as it is still under construction - with 57 (56 core, 1 distant) out of a total planned 102 (96 core, 6 distant) mini-arrays online at the time of observation - to get a first look at the low-frequency sky with NenuFAR. One of its targets is the Coma galaxy cluster: a well-known object, host of the prototype radio halo. It also hosts other features of scientific import, including a radio relic, along with a bridge of emission connecting it with the halo. It is thus a well-studied object. In this paper, we show the first confirmed NenuFAR detection of the radio halo and radio relic of the Coma cluster at 34.4 MHz, with associated intrinsic flux density estimates: we find an integrated flux value of 106.3 +- 3.5 Jy for the radio halo, and 102.0 +- 7.4 Jy for the radio relic. These are upper bound values, as they do not include point-source subtraction. We also give an explanation of the technical difficulties encountered in reducing the data, along with steps taken to resolve them. This will be helpful for other scientific projects which will aim to make use of standalone NenuFAR imaging observations in the future., Comment: 14 pages, 4 figures, special issue of the Galaxies journal

The central dark-matter fraction of galaxies is sensitive to feedback processes during galaxy formation. Strong gravitational lensing has been effective in the precise measurement of the dark-matter fraction inside massive early-type galaxies. Here, we compare the projected dark-matter fraction of early-type galaxies inferred from the SLACS strong-lens survey, with those obtained from the EAGLE, Illustris, and IllustrisTNG hydro-dynamical simulations. Previous comparisons with some simulations revealed a large discrepancy, with considerably higher inferred dark-matter fractions -- by factors 2-3 -- inside half of the effective radius in observed strong-lens galaxies as compared to simulated galaxies. Here, we report good agreement between EAGLE and SLACS for the dark-matter fractions inside both half of the effective radius and the effective radius as a function of the galaxy's stellar mass, effective radius, and total mass-density slope. However, for IllustrisTNG and Illustris, the dark-matter fractions are lower than observed. This work consistently assumes a Chabrier IMF, which suggests that a different IMF (although not excluded) is not necessary to resolve this mismatch. The differences in the stellar feedback model between EAGLE and Illustris and IllustrisTNG, are likely the dominant cause of the difference in their dark-matter fraction, and density slope., Comment: Matches with the published version. Fixed an error in Fig 2. Updated reference. Conclusions unchanged. 7 pages, 4 figures

This paper studies binary linear programming problems in the presence of uncertainties that may cause solution values to change during implementation. This type of uncertainty, termed implementation uncertainty, is modeled explicitly affecting the decision variables rather than model parameters. The binary nature of the decision variables invalidates the use of the existing models for this type of uncertainty. The robust solutions obtained are optimal for a worst-case min-max objective and allow a controlled degree of infeasibility with respect to the associated deterministic problem. Structural properties are used to reformulate the problem as a mixed-integer linear binary program. The degree of solution conservatism is controlled by combining both constraint relaxation and cardinality-constrained parameters. Solutions for optimization problems under implementation uncertainty consist of a set of robust solutions; the selection of solutions from this possibly large set is formulated as an optimization problem over the robust set. Results from an experimental study in the context of the knapsack problem suggest the methodology yields solutions that perform well in terms of objective value and feasibility. Furthermore, the selection approach can identify robust solutions that possess desirable implementation characteristics., Comment: 31 pages, 5 figures, 6 tables

Strongly lensed quasars can provide measurements of the Hubble constant ($H_{0}$) independent of any other methods. One of the key ingredients is exquisite high-resolution imaging data, such as Hubble Space Telescope (HST) imaging and adaptive-optics (AO) imaging from ground-based telescopes, which provide strong constraints on the mass distribution of the lensing galaxy. In this work, we expand on the previous analysis of three time-delay lenses with AO imaging (RXJ1131-1231, HE0435-1223, and PG1115+080), and perform a joint analysis of J0924+0219 by using AO imaging from the Keck Telescope, obtained as part of the SHARP (Strong lensing at High Angular Resolution Program) AO effort, with HST imaging to constrain the mass distribution of the lensing galaxy. Under the assumption of a flat $\Lambda$CDM model with fixed $\Omega_{\rm m}=0.3$, we show that by marginalizing over two different kinds of mass models (power-law and composite models) and their transformed mass profiles via a mass-sheet transformation, we obtain $\Delta t_{\rm BA}h\hat{\sigma}_{v}^{-2}=6.89\substack{+0.8\\-0.7}$ days, $\Delta t_{\rm CA}h\hat{\sigma}_{v}^{-2}=10.7\substack{+1.6\\-1.2}$ days, and $\Delta t_{\rm DA}h\hat{\sigma}_{v}^{-2}=7.70\substack{+1.0\\-0.9}$ days, where $h=H_{0}/100~\rm km\,s^{-1}\,Mpc^{-1}$ is the dimensionless Hubble constant and $\hat{\sigma}_{v}=\sigma^{\rm ob}_{v}/(280~\rm km\,s^{-1})$ is the scaled dimensionless velocity dispersion. Future measurements of time delays with 10% uncertainty and velocity dispersion with 5% uncertainty would yield a $H_0$ constraint of $\sim15$% precision., Comment: 11 pages, 7 figures

We study one-parameter analytic integrable deformations of the germ of $2\times(n-2)$-type complex saddle singularity given by $d(xy)=0$ at the origin $0 \in \mathbb C^2\times \mathbb C^{n-2}$. Such a deformation writes ${\omega}^t=d(xy) + \sum\limits_{j=1}^\infty t^j \omega_j$ where $t\in \mathbb C,0$ is the parameter of the deformation and the coefficients $\omega_j$ are holomorphic one-forms in some neighborhood of the origin $0\in \mathbb C^n$. We prove that, under a nondegeneracy condition of the singular set of the deformation, with respect to the fibration $d(xy)=0$, the existence of a holomorphic first integral for each element ${\omega}^t$ of the deformation is equivalent to the vanishing of certain line integrals $\oint_{\gamma_c}{\omega}^t=0, \forall \gamma_c, \forall t$ calculated on cycles $\gamma_c$ contained in the fibers $xy=c, \,0 \ne c \in \mathbb C,0$. This result is quite sharp regarding the conditions of the singular set and on the vanishing of the integrals in cycles. It is also not valid for ramified saddles, i.e., for deformations of saddles of the form $x^ny^m=c$ where $n+m>2$. As an application of our techniques we obtain a criteria for the existence of first integrals for integrable codimension one deformations of quadratic analytic center-cylinder type singularities in terms of the vanishing of some easy to compute line integrals.

When gravitational waves pass near massive astrophysical objects, they can be gravitationally lensed. The lensing can split them into multiple wave-fronts, magnify them, or imprint beating patterns on the waves. Here we focus on the multiple images produced by strong lensing. In particular, we investigate strong lensing forecasts, the rate of lensing, and the role of lensing statistics in strong lensing searches. Overall, we find a reasonable rate of lensed detections for double, triple, and quadruple images at the LIGO--Virgo--KAGRA design sensitivity. We also report the rates for A+ and LIGO Voyager and briefly comment on potential improvements due to the inclusion of sub-threshold triggers. We find that most galaxy-lensed events originate from redshifts $z \sim 1-4$ and report the expected distribution of lensing parameters for the observed events. Besides forecasts, we investigate the role of lensing forecasts in strong lensing searches, which explore repeated event pairs. One problem associated with the searches is the rising number of event pairs, which leads to a rapidly increasing false alarm probability. We show how knowledge of the expected galaxy lensing time delays in our searches allow us to tackle this problem. Once the time delays are included, the false alarm probability increases linearly (similar to non-lensed searches) instead of quadratically with time, significantly improving the search. For galaxy cluster lenses, the improvement is less significant. The main uncertainty associated with these forecasts are the merger-rate density estimates at high redshift, which may be better resolved in the future.