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At least 55 records · Page 3

Numerical simulations of colliding jets in an external wind: application to 3C 75

ABSTRACT The radio galaxy 3C 75 is remarkable because it contains a pair of radio-loud active galaxies, each of which produces a two-sided jet, with the jet beams appearing to collide and merge to the west of the galaxies. Motivated by 3C 75, we have conducted three-dimensional hydrodynamic simulations of jet collisions. We have extended previous studies by modelling the physical properties of the cluster atmosphere, including an external wind, and using realistic jet powers obtained from observational data. We are able to produce a morphology similar to that of 3C 75. The simulations imply that direct contact between the bulk jet flows on the west of the source is required to produce a morphology consistent with 3C 75. We quantify how the merging jets decelerate, how the wind deflects the jets and cocoons, the entrainment of intra-cluster material into the cocoons, the cocoon energetics, and how the jet interactions generate enstrophy. By comparing simulations of pairs of two-sided jets with those of single two-sided sources, we determine how the interaction between two bipolar jets changes their evolution. The unprecedented sensitivity and angular resolution of upcoming observatories will lead to the detection of many more complex sources at high redshift, where interacting jets are expected to be more numerous. The morphology of these complex sources can provide significant insight into the conditions in their environments.

Musoke, G.↗

Continuous Filament Network of the Local Universe

Simulated galaxy distributions are suitable for developing filament detection algorithms. However, samples of observed galaxies, being of limited size, cause difficulties that lead to a discontinuous distribution of filaments. We created a new galaxy filament catalog composed of a continuous cosmic web with no lone filaments. The core of our approach is a ridge filter used within the framework of image analysis. We considered galaxies from the HyperLeda database with redshifts 0.02 ≤ z ≤ 0.1, and in the solid angle 120° ≤ R.A. ≤ 240°, 0° ≤ decl. ≤ 60°. We divided the sample into 16 two-dimensional celestial projections with redshift bin Δ z = 0.005, and compared our continuous filament network with a similar recent catalog covering the same region of the sky. We tested our catalog on two application scenarios. First, we compared the distributions of the distances to the nearest filament of various astrophysical sources (Seyfert galaxies and other active galactic nuclei, radio galaxies, low-surface-brightness galaxies, and dwarf galaxies), and found that all source types trace the filaments well, with no systematic differences. Next, among the HyperLeda galaxies, we investigated the dependence of the g - r color distribution on the distance to the nearest filament, and confirmed that early-type galaxies are located on average further from the filaments than late-type ones.

79 ASTRONOMY AND ASTROPHYSICS↗

The Two-sided Jet Structures of NGC 1052 at Scales from 300 to 4 × 10{sup 7} Schwarzschild Radii

We investigated the jet width profile with distance along the jet in the nearby radio galaxy NGC 1052 at radial distances between ∼300 and 4 × 10{sup 7} Schwarzschild radii (R {sub S}) from the central engine on both their approaching and receding jet sides. The width of jets was measured in images obtained with the Very Long Baseline Interferometry (VLBI) Space Observatory Programme, the Very Long Baseline Array, and the Very Large Array. The jet width profiles of receding jets are apparently consistent with those of approaching jets throughout the measuring distance ranges, indicating symmetry at least up to the sphere of gravitational influence of the central black hole. The power-law index a of the jet width profile (w {sub jet} ∝ r {sup a}, where w {sub jet} is the jet width, r is the distance from the central engine in the unit of R {sub S}) apparently shows a transition from a ∼ 0 to a ∼ 1, i.e., the cylindrical-to-conical jet structures, at a distance of ∼1 × 10{sup 4} R {sub S}. The cylindrical jet shape at small distances is reminiscent of the innermost jets in 3C 84. Both the central engines of NGC 1052 and 3C 84 are surrounded by dense material, part of which is ionized and causes heavy free–free absorption.

79 ASTRONOMY AND ASTROPHYSICS↗

Limits on X-Ray Polarization at the Core of Centaurus A as Observed with the Imaging X-Ray Polarimetry Explorer

We present measurements of the polarization of X-rays in the 2–8 keV band from the nucleus of the radio galaxy Centaurus A (Cen A), using a 100 ks observation from the Imaging X-ray Polarimetry Explorer (IXPE). Nearly simultaneous observations of Cen A were also taken with the Swift, NuSTAR, and INTEGRAL observatories. No statistically significant degree of polarization is detected with IXPE. These observations have a minimum detectable polarization at 99% confidence (MDP 99 ) of 6.5% using a weighted, spectral model-independent calculation in the 2–8 keV band. The polarization angle ψ is consequently unconstrained. Spectral fitting across three orders of magnitude in X-ray energy (0.3–400 keV) demonstrates that the SED of Cen A is well described by a simple power law with moderate intrinsic absorption (N H ~ 10 23 cm -2 ) and a Fe Kα emission line, although a second unabsorbed power law is required to account for the observed spectrum at energies below 2 keV. This spectrum suggests that the reprocessing material responsible for this emission line is optically thin and distant from the central black hole. Our upper limits on the X-ray polarization are consistent with the predictions of Compton scattering, although the specific seed photon population responsible for the production of the X-rays cannot be identified. The low polarization degree, variability in the core emission, and the relative lack of variability in the Fe Kα emission line support a picture where electrons are accelerated in a region of highly disordered magnetic fields surrounding the innermost jet.

79 ASTRONOMY AND ASTROPHYSICS↗

CoLoRe: fast cosmological realisations over large volumes with multiple tracers

We present CoLoRe, a public software package to efficiently generate synthetic realisations of multiple cosmological surveys.CoLoRe can simulate the growth of structure with different degrees of accuracy, with the current implementation supporting lognormal fields, first, and second order Lagrangian perturbation theory.CoLoRe simulates the density field on an all-sky light-cone up to a desired maximum redshift, and uses it to generate multiple 2D and 3D maps: galaxy positions and velocities, lensing (shear, magnification, convergence), integrated Sachs-Wolfe effect, line intensity mapping, and line of sight skewers for simulations of the Lyman-α forest. We test the accuracy of the simulated maps against analytical theoretical predictions, and showcase its performance with a multi-survey simulation including DESI galaxies and quasars, LSST galaxies and lensing, and SKA intensity mapping and radio galaxies. We expect CoLoRe to be particularly useful in studies aiming to characterise the impact of systematics in multi-experiment analyses, quantify the covariance between different datasets, and test cross-correlation pipelines for near-future surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

Exemplary Merging Clusters: Weak-lensing and X-Ray Analysis of the Double Radio Relic, Merging Galaxy Clusters MACS J1752.0+4440 and ZWCL 1856.8+6616

We report the investigation of merging galaxy clusters that exhibit radio relics is strengthening our understanding of the formation and evolution of galaxy clusters, the nature of dark matter, the intracluster medium, and astrophysical particle acceleration. Each merging cluster provides only a single view of the cluster formation process, and the variety of merging clusters is vast. Clusters hosting double radio relics are rare and extremely important because they allow tight constraints on the merger scenario. We present a weak-lensing and X-ray analysis of MACS J1752.0+4440 (z = 0.365) and ZWCL 1856.8+6616 (z = 0.304), two double radio relic clusters. Our weak-lensing mass estimates show that each cluster is a major merger with approximately 1:1 mass ratio. The total mass of MACS J1752.0+4440 (ZWCL 1856.8+6616) is M 200 =14.7 $_{-3.3}+{+3.8}$ x 10 14 M ⊙ M 200 = 2.4 $_{-0.7}^{+0.9}$ 10 14 M ⊙ ). We find that these two clusters have comparable features in their weak-lensing and gas distributions, even though the systems have vastly different total masses. From the likeness of the X-ray morphologies and the remarkable symmetry of the radio relics, we propose that both systems underwent nearly head-on collisions. However, revelations from the hot-gas features and our multiwavelength data analysis suggest that ZWCL 1856.8+6618 is likely at a later merger phase than MACS J1752.0+4440. We postulate that the SW radio relic in MACS J1752.0+4440 is a result of particle reacceleration.

79 ASTRONOMY AND ASTROPHYSICS↗

Infrared spectroscopy of nearby radio active early-type galaxies - II: spectral atlas

ABSTRACT We present a near-infrared spectroscopic atlas of nearby, bright early-type galaxies with radio emission, containing 163 galaxies observed by the Palomar 200″ TripleSpec instrument, measuring the emission line fluxes for H, He, [Fe ii], and H2 and determined the nuclear excitation mechanisms. By stacking spectra, we deduced the H2 excitation temperature (1957 ± 182 K) and dominant excitation mechanism (thermal and shock heating combined) from the K-band emission line sequence. Stacking also produces an ‘average’ spectrum of absorption features and spectral indices from the literature; the CO12 absorption line index versus J − K colour shows a trend of stronger nuclear activity producing a weaker CO12 index and a redder (flatter) continuum. The correlations between the radio and the emission-line luminosities finds a trend with radio power; however, the large scatter in the upper limits shows that the two are not directly coupled and the duty cycles of SF and AGN activity are not synchronized.

79 ASTRONOMY AND ASTROPHYSICS↗

Powerful Radio Sources in the Southern Sky. I. Optical Identifications

Since the early sixties, our view of radio galaxies and quasars has been drastically shaped by discoveries made thanks to observations of radio sources listed in the Third Cambridge Catalog and its revised version (3CR). However, the largest fraction of data collected to date on 3CR sources was performed with relatively old instruments, rarely repeated and/or updated. Importantly, the 3CR contains only objects located in the Northern Hemisphere, thus having limited access to new and innovative astronomical facilities. To mitigate these limitations, we present a new catalog of powerful radio sources visible from the Southern Hemisphere, extracted from the GLEAM 4 Jy (G4Jy) catalog and based on equivalent selection criteria as the 3CR. This new catalog, named G4Jy-3CRE, where the E stands for “equivalent,” lists a total of 264 sources at decl. below -5° and with 9 Jy limiting sensitivity at ~178 MHz. We explored archival radio maps obtained with different surveys and compared them with optical images available in the Pan-STARRS, DES, and DSS databases to search for optical counterparts of their radio cores. We compared mid-infrared counterparts, originally associated in the G4Jy, with the optical ones identified here, and we present results of a vast literature search carried out to collect redshift estimates for all G4Jy-3CRE sources resulting in a total of 145 reliable z measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

FAST Discovery of a Fast Neutral Hydrogen Outflow

Abstract In this letter, we report the discovery of a fast neutral hydrogen outflow in SDSS J145239.38+062738.0, a merging radio galaxy containing an optical type I active galactic nucleus (AGN). This discovery was made through observations conducted by the Five-hundred-meter Aperture Spherical radio Telescope (FAST) using redshifted 21 cm absorption. The outflow exhibits a blueshifted velocity likely up to ∼−1000 km s −1 with respect to the systemic velocity of the host galaxy with an absorption strength of ∼−0.6 mJy beam −1 corresponding to an optical depth of 0.002 atv= −500 km s −1 . The mass outflow rate ranges between 2.8 × 10 −2 and 3.6M ⊙ yr −1 , implying an energy outflow rate ranging between 4.2 × 10 39 and 9.7 × 10 40 erg s −1 , assuming 100 K s< 1000 K. Plausible drivers of the outflow include the starbursts, AGN radiation, and radio jet, the last of which is considered the most likely culprit according to the kinematics. By analyzing the properties of the outflow, AGN, and jet, we find that if the Hioutflow is driven by the AGN radiation, the AGN radiation does not seem powerful enough to provide negative feedback, whereas the radio jet shows the potential to provide negative feedback. Our observations contribute another example of a fast outflow detected in neutral hydrogen and demonstrate the capability of FAST in detecting such outflows.

Astronomy & Astrophysics↗

AGNs in post-mergers from the ultraviolet near infrared optical northern survey

The kinematic disturbances associated with major galaxy mergers are known to produce gas inflows, which in turn may trigger accretion onto the supermassive black holes (SMBH) of the participant galaxies. While this effect has been studied in galaxy pairs, the frequency of active galactic nuclei (AGNs) in fully coalesced post-merger systems is poorly constrained due to the limited size or impurity of extant post-merger samples. Previously, we combined convolutional neural network (CNN) predictions with visual classifications to identify a highly pure sample of 699 post-mergers in deep r-band imaging. In the work presented here, we quantify the frequency of AGNs in this sample using three metrics: optical emission lines, mid-infrared (mid-IR) colour, and radio detection of low-excitation radio galaxies (LERGs). We also compare the frequency of AGNs in post-mergers to that in a sample of spectroscopically identified galaxy pairs. We find that AGNs identified by narrow-line optical emission and mid-IR colour have an increased incidence rate in post-mergers, with excesses of ~4 over mass- and redshift-matched controls. The optical and mid-IR AGN excesses in post-mergers exceed the values found for galaxy pairs, indicating that AGN activity in mergers peaks after coalescence. Conversely, we recover no significant excess of LERGs in post-mergers or pairs. Finally, we find that the [O III ] luminosity (a proxy for SMBH accretion rate) in post-mergers that host an optical AGN is ~0.3 dex higher on average than in non-interacting galaxies with an optical AGN, suggesting that mergers generate higher accretion rates than secular triggering mechanisms.

79 ASTRONOMY AND ASTROPHYSICS↗

Mapping the Perseus galaxy cluster with XRISM: Gas kinematic features and their implications for turbulence

We present extended gas kinematic maps of the Perseus cluster based on a combination of five new XRISM/Resolve pointings observed in 2025 with four performance verification datasets from 2024, totaling a net exposure of 745 ks. To date, Perseus remains the only cluster that has been extensively mapped out to ≃0.7 r 2500 by XRISM/Resolve, while simultaneously offering sufficient spatial resolution to resolve gaseous substructures driven by mergers and active galactic nucleus (AGN) feedback. Our observations cover multiple radial directions and a broad range of dynamical scales, enabling us to characterize the kinematic properties of the intracluster medium up to a scale of ∼500 kpc. In the measurements, we detected high-velocity dispersions (≃300km s −1 ) in the eastern region of the cluster that are spatially coincident with the extended X-ray surface brightness excess and correspond to a nonthermal pressure fraction of ≃7 − 13%. The velocity field outside the AGN-dominant region can be effectively described by a single, large-scale kinematic driver based on the velocity structure function, which statistically favors an energy injection scale of at least a few hundred kpc. The estimated turbulent dissipation energy is comparable to the gravitational potential energy released by a recent merger, implying a significant role of turbulent cascade in the merger energy conversion. In the bulk velocity field, we observed a dipole-like pattern along the east-west direction with an amplitude of ≃ ± 200 − 300 km s −1 , indicating rotational motions induced by the recent merger event. This feature constrains the viewing direction to ≃30° −50° relative to the normal of the merger plane. Our hydrodynamic simulations suggest that Perseus has experienced at least two energetic mergers since redshift z ∼ 1, the most recent of which is associated with the radio galaxy IC310, in agreement with recent SRG/eROSITA findings. This study showcases exciting scientific opportunities for future missions with high-resolution spectroscopic capabilities (e.g., HUBS, LEM, and NewAthena).

79 ASTRONOMY AND ASTROPHYSICS↗

The Fourth Catalog of Active Galactic Nuclei Detected by the Fermi Large Area Telescope: Data Release 3

Abstract An incremental version of the fourth catalog of active galactic nuclei (AGNs) detected by the Fermi Large Area Telescope is presented. This version (4LAC-DR3) derives from the third data release of the 4FGL catalog based on 12 yr of E > 50 MeV gamma-ray data, where the spectral parameters, spectral energy distributions (SEDs), yearly light curves, and associations have been updated for all sources. The new reported AGNs include 587 blazar candidates and four radio galaxies. We describe the properties of the new sample and outline changes affecting the previously published one. We also introduce two new parameters in this release, namely the peak energy of the SED high-energy component and the corresponding flux. These parameters allow an assessment of the Compton dominance, the ratio of the inverse-Compton to the synchrotron-peak luminosities, without relying on X-ray data.

79 ASTRONOMY AND ASTROPHYSICS↗

Polarization and variability of compact sources measured in Planck time-ordered data

This paper introduces a new Planck Catalog of Polarized and Variable Compact Sources (PCCS-PV) comprising 153 sources, the majority of which are extragalactic. The data include both the total flux density and linear polarization measured by Planck with frequency coverage from 30 to 353 GHz, and temporal spacing ranging from days to years. We classify most sources as beamed, extragalactic radio sources; the catalog also includes several radio galaxies, Seyfert galaxies, and Galactic and Magellanic Cloud sources, including H II regions and planetary nebulae. An advanced extraction method applied directly to the multifrequency Planck time-ordered data, rather than the mission sky maps, was developed to allow an assessment of the variability of polarized sources. Our analysis of the time-ordered data from the Planck mission, tod2flux, allowed us to catalog the time-varying emission and polarization properties for these sources at the full range of polarized frequencies employed by Planck, 30-353 GHz. PCCS-PV provides the time-and frequency-dependent, polarized flux densities for all 153 sources. To illustrate some potential applications of the PCCS-PV, we conducted preliminary comparisons of our measurements of selected sources with published data from other astronomical instruments. In summary, we find general agreement between the Planck and the Institut de Radioastronomie Millimétrique (IRAM) polarization measurements as well as with the Metsähovi 37 GHz values at closely similar epochs. Here, these combined measurements also show the value of PCCS-PV results and the PCCS2 catalog for filling in missing spectral (or temporal) coverage and helping to define the spectral energy distributions of extragalactic sources. In turn, these results provide useful clues as to the physical properties of the sources.

79 ASTRONOMY AND ASTROPHYSICS↗

Constraining models for the origin of ultra-high-energy cosmic rays with a novel combined analysis of arrival directions, spectrum, and composition data measured at the Pierre Auger Observatory

The combined fit of the measured energy spectrum and shower maximum depth distributions of ultra-high-energy cosmic rays is known to constrain the parameters of astrophysical models with homogeneous source distributions. Studies of the distribution of the cosmic-ray arrival directions show a better agreement with models in which a fraction of the flux is non-isotropic and associated with the nearby radio galaxy Centaurus A or with catalogs such as that of starburst galaxies. Here, we present a novel combination of both analyses by a simultaneous fit of arrival directions, energy spectrum, and composition data measured at the Pierre Auger Observatory. The model takes into account a rigidity-dependent magnetic field blurring and an energy-dependent evolution of the catalog contribution shaped by interactions during propagation. We find that a model containing a flux contribution from the starburst galaxy catalog of around 20% at 40 EeV with a magnetic field blurring of around 20° for a rigidity of 10 EV provides a fair simultaneous description of all three observables. The starburst galaxy model is favored with a significance of 4.5σ (considering experimental systematic effects) compared to a reference model with only homogeneously distributed background sources. By investigating a scenario with Centaurus A as a single source in combination with the homogeneous background, we confirm that this region of the sky provides the dominant contribution to the observed anisotropy signal. Models containing a catalog of jetted active galactic nuclei whose flux scales with the γ-ray emission are, however, disfavored as they cannot adequately describe the measured arrival directions.

79 ASTRONOMY AND ASTROPHYSICS↗

Carbon-loud SDSS BOSS type II quasars at z > 2: high-density gas or secondary production of carbon?

ABSTRACT We study the ultraviolet (UV) emission-line ratios of a sample of 145 type II quasars (QSO2s) from Sloan Digital Sky Survey iii Baryon Oscillation Spectroscopic Survey, and compare against a grid of active galactic nucleus (AGN) photoionization models with a range in gas density, gas chemical abundances, and ionization parameter. Most of the quasars are ‘carbon-loud’, with C iv/He ii ratios that are unusually high for the narrow-line region, implying higher than expected gas density (>106 cm−3) and/or significantly supersolar-relative carbon abundance. We also find that solar or supersolar nitrogen abundance and metallicity are required in the majority of our sample, with potentially significant variation between objects. Compared to radio galaxies at similar redshifts (HzRGs; z > 2), the QSO2s are offset to higher N v/He ii, C iv/He ii, and C iii]/He ii, suggesting systematically higher gas density and/or systematically higher C and N abundances. We find no evidence for a systematic difference in the N/C abundance ratio between the two types of objects. Scatter in the N iv]/C iv ratio implies a significant scatter in the N/C abundance ratio among the QSO2s and HzRGs, consistent with differences in the chemical enrichment histories between objects. Interestingly, we find that adopting secondary behaviour for both N and C alleviates the long-standing ‘N iv] problem’. A subset of the QSO2s and HzRGs also appear to be ‘silicon-loud’, with Si iii] relative fluxes suggesting Si/C and Si/O are an order of magnitude above their solar values. Finally, we propose new UV-line criteria to select genuine QSO2s with low-density narrow-line regions.

Silva, M.↗

An Improved Measurement of the Secondary Cosmic Microwave Background Anisotropies from the SPT-SZ + SPTpol Surveys

We report new measurements of millimeter-wave power spectra in the angular multipole range 2000 ≤ ℓ ≤ 11,000 (angular scales ). By adding 95 and 150 GHz data from the low-noise 500 deg 2 SPTpol survey to the SPT-SZ three-frequency 2540 deg 2 survey, we substantially reduce the uncertainties in these bands. These power spectra include contributions from the primary cosmic microwave background, cosmic infrared background, radio galaxies, and thermal and kinematic Sunyaev–Zel'dovich (SZ) effects. The data favor a thermal SZ (tSZ) power at 143 GHz of and a kinematic SZ (kSZ) power of . This is the first measurement of kSZ power at ≥3 σ . However, different assumptions about the CIB or SZ models can reduce the significance down to 2.4 σ in the worst case. We study the implications of the measured kSZ power for the epoch of reionization under the Calabrese et al. model for the kSZ power spectrum and find the duration of reionization to be ( at 95% confidence), when combined with our previously published tSZ bispectrum measurement. The upper limit tightens to if the assumed homogeneous kSZ power is increased by 25% (~0.5 μ K 2 ) and relaxes to if the homogeneous kSZ power is decreased by the same amount.

79 ASTRONOMY AND ASTROPHYSICS↗

An Improved Measurement of the Secondary Cosmic Microwave Background Anisotropies from the SPT-SZ + SPTpol Surveys

We report new measurements of millimeter-wave power spectra in the angular multipole range $2000 \le \ell \le 11,000$ (angular scales $5^\prime \gtrsim \theta \gtrsim 1^\prime$). By adding 95 and 150\,GHz data from the low-noise 500 deg$^2$ SPTpol survey to the SPT-SZ three-frequency 2540 deg$^2$ survey, we substantially reduce the uncertainties in these bands. These power spectra include contributions from the primary cosmic microwave background, cosmic infrared background, radio galaxies, and thermal and kinematic Sunyaev-Zel'dovich (SZ) effects. The data favor a thermal SZ (tSZ) power at 143\,GHz of $D^{\rm tSZ}_{3000} = 3.42 \pm 0.54~ \mu {\rm K}^2$ and a kinematic SZ (kSZ) power of $D^{\rm kSZ}_{3000} = 3.0 \pm 1.0~ \mu {\rm K}^2$. This is the first measurement of kSZ power at $\ge 3\,\sigma$. We study the implications of the measured kSZ power for the epoch of reionization, finding the duration of reionization to be $\Delta z_{re} = 1.0^{+1.6}_{-0.7}$ ($\Delta z_{re}< 4.1$ at 95% confidence), when combined with our previously published tSZ bispectrum measurement.

79 ASTRONOMY AND ASTROPHYSICS↗

SPT-3G D1: A Measurement of Secondary Cosmic Microwave Background Anisotropy Power

We report new measurements of millimeter-wave temperature power spectra in the angular multipole range $1700 \le \ell \le 11,000$ (wavelengths $13^\prime \gtrsim λ\gtrsim 2^\prime$). We use two years of data in three observing bands centered near 95, 150, and 220 GHz from the SPT-3G receiver on the South Pole Telescope that cover a 1646 deg$^2$ region of the Southern sky. Using the measured power spectra, we present constraints on the thermal and kinematic Sunyaev-Zel'dovich (SZ) effects, radio galaxies, and cosmic infrared background (CIB). We find that inferred SZ powers are dependent on the detailed modeling of the thermal SZ-CIB correlation, and to a lesser extent on the assumed angular dependence of the SZ spectra. We report constraints for simulation-based model templates as well as fits where the angular dependencies of the SZ and CIB power spectra are allowed to vary. In the latter case at $\ell=3000$, we find thermal SZ power at 143 GHz of $D_{3000}^{\rm tSZ} = 4.91\pm0.37\, μ{\rm K}^2$ and kinematic SZ power of $D_{3000}^{\rm kSZ} =1.75\pm0.86\, μ{\rm K}^2$. We use the measured kinematic SZ power to estimate the duration of reionization, noting that the reionization inferences are sensitive to the model choices and assumed level of homogeneous kinematic SZ power from the late-time universe. We find a 95% limit on the duration from an ionization fraction of 25% to 75% of $Δ^{50} z_{\rm re} <\,3.8$ based on a semi-analytic model, or a limit on the duration from an ionization fraction of 5% to 95% of $Δ^{90} z_{\rm re} <\,6.1$ based on the AMBER simulations.

Chaubal, P. [Melbourne U.]↗