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Sunday 27 September

High Energy Astrophysical Phenomena · Cross-listed from gr-qc

Stochastic gravitational-wave background from self-interacting superradiant clouds

Gravitational-wave (GW) observations offer a powerful probe of new fundamental fields. One well-motivated source is black hole (BH)–boson cloud systems, in which an ultralight scalar field forms a cloud around a rotating BH via superradiance and emits long-lived nearly monochromatic GWs. In this work, we compute the stochastic GW background (SGWB) from such systems, extending previous work by including scalar self-interactions, and discuss its detectability with next-generation ground-based GW detectors. We find that self-interactions can suppress the SGWB and thereby relax existing LIGO-Virgo-KAGRA constraints inferred from null searches. Namely, the LIGO detectors at design sensitivity are insensitive to a SGWB produced by scalar fields with a decay constant $f_\mathrm{s} \lesssim 3\times 10^{17}$ GeV, independently of the scalar field mass. Looking ahead, we show that a moderately self-interacting cloud can still produce a detectable SGWB with next-generation detectors. Under conservative assumptions, for a decay constant $f_\mathrm{s} = 10^{17}$ GeV, the Einstein Telescope (ET) will be sensitive to scalar masses in the range $\sim[10^{-13.0},10^{-11.8}]$ eV, while Cosmic Explorer (CE) will be sensitive to scalar masses in the range $\sim[10^{-13.2},10^{-11.7}]$ eV. We also find that the minimum decay constants that still yield a detectable SGWB for ET and CE are $f_\mathrm{s}\sim 6\times10^{16}\,$GeV and $\sim 3\times10^{16}\,$GeV, respectively.
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High Energy Astrophysical Phenomena

Evidence for an extended Galactic proton component beyond the cosmic-ray knee

The cosmic-ray (CR) knee at a few petaelectronvolts (PeV) is commonly associated with the acceleration limit of Galactic protons. Recent detection of multi-PeV photons from the microquasar Cygnus X-3 suggests proton acceleration to tens of PeV. However, the contribution of such type of sources to CRs remains unclear. Here we analyse proton and helium spectral data spanning from 0.1 to 1000~PeV and find that the knee strongly disfavours a single terminal cutoff. Full-spectrum analyses incorporating measurements down to tens of gigaelectronvolts (GeV) require a proton contribution extending beyond $100\,\mathrm{PeV}$. This contribution either extends continuously from GeV to 100~PeV energies or belongs to a distinct component whose spectrum has a spectral break at the knee. Within source-population interpretations, its connection to lower-energy Galactic cosmic rays suggests a Galactic origin. The component from GeV energies is conventionally associated with supernova remnants, but extending it beyond $100\,\mathrm{PeV}$ challenges acceleration theory and $\gamma$-ray observations of ordinary remnants . A spectral break, by contrast, can arise naturally from rigidity-dependent transport. This interpretation makes the knee a probe of Galactic CR transport, and connects the extended proton spectrum to extreme Galactic accelerators, such as super-Eddington X-ray binaries, that can also produce PeV $\gamma$ rays and neutrinos.
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Solar and Stellar Astrophysics

Modeling of the variability of D-region ionospheric electron density during solar cycle-24

Solar cycle variation of earth's atmosphere, particularly the ionosphere is of particular interest in the field of space science and space weather studies. In this article, we present the outcome of our detailed quantitative study on solar cycle variation of lower ionospheric properties using numerical investigation. First, we seek to model and compare the collective D-region ionization rates (q's) due to the individual contributions from the ionizing sources, namely, (a) solar extreme ultraviolet (EUV) radiation including the Lyman-alpha irradiation and (b) solar X-ray irradiation throughout the 24th solar cycle (C24). Then, we compute the electron density (Ne) profiles using the ionization rates. We report significant solar cycle variation in ionization rate and electron density profiles for the entire span of C24. We use the sunspot number (SPN) profile to substantiate the finer details of Ne profile during C24. For the segments of the D-region above two different geographic coordinates, we report that Ne profiles show a consistent "dual peak" nature. It is very similar to the SPN profile during C24. As a next-order validation, we compare our modeled Ne profiles with their IRI-2020 counterpart (Ne,iris). Their overall trends are found to be in agreement. Finally, we discuss the response of the D-region in terms of Ne due to C24. The work lays the foundation for our upcoming studies on D-region response to solar cycle variation with Very Low Frequency (VLF) observation.
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All authors Sayak Chakraborty, Sourav Palit, Semontee Deb, Tamal Basak

Astrophysics of Galaxies

Barred Galaxies in MaNGA: Stellar Mass Dependence and Black Hole Growth

This study investigates the role of internal structures, such as stellar bars and active galactic nuclei (AGN), in shaping galaxy evolution using 7,408 galaxies (2,641 barred) from the SDSS-IV MaNGA survey. Our analysis spans a wide stellar mass range, from dwarf to massive galaxies, examining how internal and environmental processes regulate galaxy evolution. Galaxies are categorized by morphology (ellipticals (E), lenticulars (S0s), early-type spirals (ETS), and late-type spirals (LTS)), environment, and the presence of a bar. We find that barred galaxies have higher median specific star formation rate (sSFR) than unbarred galaxies across most stellar mass intervals. This difference varies with host morphology, with LTS and S0 galaxies showing different trends across stellar mass intervals. The environmental trends of barred and unbarred galaxies are broadly similar within the same mass intervals. In AGN hosts, barred Seyferts tend to lie near the star-forming$-$green valley boundary, while barred LINERs preferentially occupy the green valley. We further examine the relation between stellar bars and black hole mass and find that barred galaxies host systematically lower black hole masses than unbarred galaxies, with environmental effects appearing to play a secondary role in shaping these differences. A multivariate regression analysis also shows that the positive bar$-$sSFR association remains statistically significant for star-forming galaxies after accounting for stellar mass, local density, AGN activity, and morphology. Our results highlight the interconnected roles of stellar bars, stellar mass, morphology, and environment in shaping galaxy star formation, providing new insights into the role of stellar bars in galaxy evolution.
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Astrophysics of Galaxies

CHANG-ES XLII: Cosmic-Ray Electron Transport and the Spatially Resolved Radio-SFR Relation in Edge-on Galaxies

Radio continuum emission traces star formation in galaxies, but cosmic-ray electron (CRE) propagation between the disk and halo complicates this connection. We present a wide-band, spatially resolved analysis of 19 nearby edge-on galaxies, combining LOFAR observations at 144 MHz with CHANG-ES VLA imaging at 1.575, 3.0, and 6.0 GHz, and hybrid H$\alpha$+22 $\mu$m star formation rate (SFR) maps. All maps are convolved to a common 2.1 kpc resolution for pixel-by-pixel analysis of the nonthermal spectral index $\alpha_{\mathrm{nth}}$ and the SFR surface density $\Sigma_{\mathrm{SFR}}$. All 19 galaxies exhibit statistically significant nonthermal spectral flattening with increasing $\Sigma_{\mathrm{SFR}}$, with a sample median slope of $0.19_{-0.03}^{+0.09}$ that traces the contrast between CRE injection in the star-forming disk and cooling in the halo. The galaxy-to-galaxy scatter in this slope shows no dependence on global galaxy properties and instead appears to be modulated by the local dynamical environment, with the largest $\alpha_{\mathrm{nth}}$-$\Sigma_{\mathrm{SFR}}$ slopes appearing in tidally perturbed systems. The resolved radio-SFR slope steepens from 0.57 at 144 MHz to 0.95 at 6 GHz, approaching linearity at high frequencies. This trend is consistent with energy-dependent CRE cooling and transport, with the deviation from linearity most pronounced at low frequencies, where the edge-on line of sight blends midplane and halo CRE populations. These results are robust against thermal contamination, beam smearing, and spectral curvature. Together, our analysis establishes $\alpha_{\mathrm{nth}}$ as an observational probe of projected disk-to-halo CRE transport in edge-on galaxies and quantifies how this transport reshapes the frequency dependence of resolved radio-SFR calibrations.
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All authors Jianghui Xu, Volker Heesen, Jiang-Tao Li, Guilin Liu, Rainer Beck, Li-Yuan Lu, Yang Yang, Jayanne English, Shengtao Wang

High Energy Astrophysical Phenomena

Testing Spin Prior Assumptions of Binary Black Hole Parameter Inference and Their Astrophysical Implications

With the growing number of binary black hole (BBH) candidates in the Gravitational-Wave Transient Catalog 5.0 (GWTC-5.0), an increasing number of BBH systems with distinct properties have been reported. The individual spins are relatively less constrained in the parameter estimations for most events. While the LIGO-Virgo-KAGRA Collaboration (LVK) adopts a uninformative spin prior by default, some binary evolution scenarios have strong predictions on component spins. In this work, we perform Bayesian parameter inference for a subset of BBH events spanning a broad range of properties in the chirp mass, mass ratio, and effective inspiral spin ($\mathcal{M}_{\rm c}$-$q$-$\chi_{\rm eff}$) parameter space. We consider three different spin priors: the LVK spin prior and two astrophysically motivated priors, assuming a non-spinning primary BH ($\chi_1 = 0$) or a non-spinning secondary BH ($\chi_2 = 0$). We find that the non-spinning primary BH prior is disfavored by the data for several systems with high effective inspiral spins, including GW190517_055101, GW190412, GW241113_163507, and GW231028_153006. We suggest that standard common-envelope evolution represents a promising formation channel that can be tested with gravitational-wave observations, and propose a novel method for estimating the merger rate of systems formed through alternative evolutionary channels. We further suggest that the binary evolution involving mass-ratio reversal may provide a possible formation pathway for these systems.
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All authors Chen-He Wu, Wei-Hua Guo, Shu-Jin Hou, Yuan-Zhu Wang, Ying Qin

High Energy Astrophysical Phenomena · Cross-listed from hep-ph

Probing Solar Chameleons with XENONnT Ionization-Only Data

Screened scalar fields provide a possible connection between dark energy and laboratory-scale new physics while remaining compatible with existing fifth-force constraints. Solar production offers a direct probe of these models, and ionization-only measurements extend the sensitivity of liquid-xenon detectors into the sub-keV regime. We present the first search for solar chameleons using low-energy S2-only data, based on the 7.83 tonne-year XENONnT ionization-only data set. The predicted electronic-recoil spectrum is folded through the run-dependent detector response and tested directly in corrected-S2 (cS2) space. A joint binned likelihood combines the seven cS2 bins of science runs SR0, SR1, and SR2. We sample the five-dimensional parameter space $\{\beta_e,\beta_\gamma,M_e,\Lambda,n\}$ and derive posterior constraints on the conformal and disformal electron couplings. The data extend the recoil-energy reach to approximately $0.04~{\rm keV}_{ee}$, where the few-electron detector response and instrumental backgrounds must be modeled explicitly. In the disformal-dominated regime, the result is expressed in terms of $\beta_{\rm eff}\equiv\beta_\gamma({\rm eV}/M_e)^4$. We obtain the upper limit $\log_{10}\beta_{\rm eff}<-3.64$. Although the present analysis reaches a lower energy threshold than our previous XENONnT electronic-recoil analysis, the resulting constraint is weaker, primarily because the disformal absorption rate decreases rapidly toward low recoil energies, where the background rate also becomes larger. This analysis establishes low-energy ionization data as a new experimental channel for testing solar chameleons and screened dark-energy models.
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Earth and Planetary Astrophysics

The July 2023 Outburst of Comet 12P/Pons-Brooks: Observations and Modeling of Dust Coma and Arc Structure

We conducted continuous imaging observations of comet 12P/Pons-Brooks, which has experienced multiple outbursts since 2023 July. Among these, we determined the dust coma expansion velocities and the occurrence times for three outbursts. The outburst on 2023 July 20.39$\pm$0.05 had an expansion velocity of 207.5$\pm$0.1 m s$^{-1}$. The outburst on 2023 November 14.52$\pm$0.10 had an expansion velocity of 305.8$\pm$13.7 m s$^{-1}$, and the outburst on April 2.23$\pm$0.06, 2024 had an expansion velocity of 408.9$\pm$14.3 m s$^{-1}$. During the July outburst, in addition to the isotropically expanding dust coma, a semicircular structure (arc structure) was observed. This structure expanded without changing shape over two months, until mid-September, at a slower velocity of 52.0$\pm$1.7 m s$^{-1}$ compared to the outer coma. We hypothesize that this arc structure consists of dust ejected over a certain period during the outburst from an active region at mid-latitudes on the comet's nucleus, with a rotation axis near the line of sight. We performed model calculations to reproduce the structure. As a result, we found that the observations were well reproduced by assuming a rotation axis direction of RA = $85^\circ$, Dec = $-30^\circ$ to $-35^\circ$ and an active region latitude of $70^\circ$ during the July outburst. The active period of the outburst was shorter than the rotation period, approximately 0.7 times the rotation period. Since the dust particles comprising the arc structure escaped dissipation due to solar radiation pressure, we infer that they are dust with a ratio of radiation pressure to gravity of $\beta \sim 0.1$, which corresponds to a dust particle size of about $10\,\mu\mathrm{m}$.
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All authors Hitoshi Hasegawa, Mitsunori Tsumura, Shin-ichi Watanabe, Hiroki Akisawa, Jun-ichi Watanabe

Earth and Planetary Astrophysics

On the Secular Evolution of Inclinations Among the Classical Belt TNOs

Proper orbital elements have been used in diverse ways to study the dynamical architecture of transneptunian objects (TNOs), providing insights into Solar System evolution and migration theories. In this paper, we present the numerically-computed proper elements of all known TNOs. We then compare their distribution with the distribution of proper elements of a large synthetic sample generated to study the secular behavior of TNOs in the Classical belt region in an effort to better understand certain observed features, particularly features appearing in the inclination distribution of these TNOs. Our analysis indicates the presence of an inclination-dependent instability in the Classical belt from 42 < a < 45 au, which we find is caused by the g+s-g8-s8 = 0 secular resonance. The coincidence of this instability with the previously-noted inclination boundary of the Cold Classical belt near proper inclination of Ifree = 4 (deg) could suggest that the primordial Classical belt may have originally been more continuous between 4 < Ifree (deg) < 6 than we observe today. However, our analysis to account for the impact of secular resonant instabilities finds a best-estimate of the inclination width of the primordial Cold Classical belt near 1.5(deg), well below 4(deg), and slightly thinner than previous works have suggested. We conclude that the inclination boundary of the Cold Classical belt is not set directly by secular resonance or instability, and that this belt is generally unaltered by resonance or instability since the end of planetary migration.
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All authors Dallin Spencer, Darin Ragozzine, Kat Volk, Renu Malhotra

2609.33080 · 27 Sep · 26 pages, 10 figures, and 2 tables. Submitted to The Astronomical Journal, pending review as of 09/26/2026. Data will be published in a Zenodo repository with the reserved doi:10.5281/zenodo.22285391. The datasets are also accessible at this presently publicly available GitHub repository: https://github.com/dallinspencer/TNO-Secular-Dynamics-Catalog/

Saturday 26 September

Instrumentation and Methods for Astrophysics

Error Propagation from Integral Moments and Spectral Derivatives of Stokes Profiles to Magnetic Observables

We aim to derive convenient analytic estimations of magnetic inference errors, which can be used to inform and facilitate the creation of the science-traceability matrix of a polarimetric instrument. In order to do this, we study the general problem of the propagation of Poissonian noise in polarized light signals to derived data products of the Stokes profiles, namely integral moments of arbitrary orders and spectral derivatives of the intensity. In particular, we derive the errors on the longitudinal and transversal projections of the magnetic field inferred from the weak-field approximation (WFA) of the Zeeman effect. The propagated errors on magnetic inference are traced back to the signal- to-noise ratio (SNR) of the observations. The results can be used to quantify the contributions of different environmental and instrumental conditions (spectral line width, spectral resolution, line spread function, stray light) to the overall error on the inferred quantities. Our tests indicate that the integral-moment method of inference is comparable to the local derivative in a predictable way.
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Instrumentation and Methods for Astrophysics · Cross-listed from gr-qc

Gravitational-Wave Modulation of Atomic Spontaneous Emission: Electrodynamical Theory, Quadrupolar Redistribution, and Rydberg Cavity Metrology

Studying Gravitational Waves (GWs) provide a unique probe of the interplay between quantum matter and the dynamics of spacetime. We develop a QED framework for spontaneous emission in the presence of a weak classical GW by quantizing the electromagnetic field in a linearized gravitational background. We show that a passing GW dynamically phase-modulates vacuum electromagnetic modes, dressing photon states into a Floquet ladder of sidebands separated by the GW frequency. While the total spontaneous decay rate remains unchanged to first order in the GW strain, the emission pattern develops a characteristic spin-2 quadrupolar angular redistribution modulated with the GW phase. For finite interaction times, interference between the carrier and Floquet sidebands generates phase-dependent spectral asymmetries in the transient emission spectrum. To explore experimental observability, we formulate a cavity-QED master equation description and propose a differential cross-cavity detection protocol employing Rydberg ensembles or highly charged ions. These results establish cavity QED as a promising platform for exploring quantum electrodynamics in dynamical spacetime and for high-frequency gravitational-wave detection.
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Earth and Planetary Astrophysics

Worlds Next Door. V. A Candidate Solar System Scale Super-Jupiter in the 61 Cygni Binary System

We present new constraints on a candidate third companion in the 61 Cygni binary system-one of the closest neighbors to our solar system (3.5 pc), the first stars to have a measured parallax, and two of the most favorable targets for habitable zone exo-Earth searches with future direct imaging missions. Kervella et al. (2022) first identified the candidate based on a 4.4$\sigma$ tangential velocity anomaly in the system determined using Hipparcos and Gaia DR3 astrometry of the A and B components. We combine this astrometric evidence with constraints from Gaia DR3 RUWE, MMT/Clio Lp imaging, nearly four decades of radial velocity (RV) measurements (including $\sim$2 years of new NEID RVs presented here), and N-body dynamical stability calculations of both stars in a Monte Carlo framework to estimate the candidate companion's mass and semi-major axis. Our analysis reveals that all of the available data are compatible with an $\approx(8 \pm 3)\;M_{\rm Jup}$ super-Jupiter in an $\approx(8 \pm 3)$ au orbit, with a broad range of allowed eccentricities and mutual inclinations. Using the Sonora Flame Skimmer evolutionary models, given the system's mature age of $(6.0 \pm 1.0)$ Gyr, we estimate a companion effective temperature of $(282 \pm 55)$ K and radius of $(1.02 \pm 0.02)\;R_{\rm Jup}$. Finally, we evaluate the stability of terrestrial planets in the habitable zone (HZ) of 61 Cygni AB in the presence of the giant planet candidate using N-body simulations. A companion semi-major axis $\lesssim$5 au, irrespective of the planet-planet mutual inclination, and between $\approx$5 au and 10 au, for misaligned orbits ($40^o \lesssim i_{\rm mut} \lesssim 140^o$), severely disrupts the HZ. Our results highlight the need to confirm the planet candidate and characterize its orbit to inform future exo-Earth searches with missions such as SHERA, HWO, and LIFE.
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All authors Aniket Sanghi, Billy Quarles, Andrea S. J. Lin, Cheyanne Shariat, Pierre Kervella, James Mang, Dimitri Mawet, Mark R. Giovinazzi, Arvind F. Gupta, Charles Beichman, Bertrand Mennesson, Mathilde Mâlin, Jerry W. Xuan, Liton Majumdar, Jack J. Lissauer, Mark Wyatt, William O. Balmer, Eduardo Bendek, Kevin Wagner

Cosmology and Nongalactic Astrophysics

Constant-Roll Inflation as a Competitive Alternative to Slow-Roll Inflation

Starting from the constant-roll condition, which involves the constant-roll parameter $\beta$, which is a fundamental constant in the constant-roll inflationary models, we derive the scalar power spectrum and obtain an analytic expression for the scalar spectral index $n_s$ in terms of $\beta$ and the number of remaining e-folds $\tilde N$. The resulting relation is non-monotonic in $\beta$, allowing two distinct constant-roll branches, one with $\beta<0$ and one with $\beta>0$, to reproduce nearly the same observed scalar tilt. We constrain $\beta$ using Planck 2018 CMB data, and further using the combined Planck 2018 + ACT DR6 data. For Planck 2018, the posterior distribution of $\beta$ exhibits a bimodal structure associated with the two analytical branches, while the combined Planck+ACT analysis tightens the allowed range of $\beta$ and shows continued consistency with the $\beta=0$ slow-roll-like spectral point. The data constrain $\beta$ to be small, but do not require it to vanish exactly. We also estimate the inflationary mass scale $M$ by using the observed scalar-amplitude normalization at the pivot scale. Both the negative and positive $\beta$ branches give a high-scale inflationary normalization of order $M\sim10^{-5}M_{\rm Pl}$. We show that the $\beta \to 0$ limit is only spectrally slow-roll like, but does not reproduce standard slow-roll dynamics. Our results show that constant-roll inflation is observationally competitive with the usual slow-roll inflationary paradigm. The constant roll inflation model is supported by the latest CMB observations equally well or marginally better when compared with the slow roll inflation model.
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Solar and Stellar Astrophysics

SolRaT: polarized spectral line modeling with multi-term and multi-level atoms

The interpretation of polarized spectral lines requires models that combine statistical equilibrium with polarized radiative transfer accounting for atomic polarization, the Hanle effect, and Zeeman and Paschen-Back splitting. The aim is to provide an open-source Python implementation of the irreducible spherical tensor formalism of Landi Degl`Innocenti and Landolfi (2004), hereafter LL04, for forward synthesis of Stokes profiles with interchangeable atomic descriptions. SolRaT solves the statistical equilibrium and polarized transfer problem for interchangeable multi-term and multi-level atomic descriptions. The multi-term model retains coherences between fine-structure levels of the same term and treats the magnetic Hamiltonian by exact diagonalization, allowing the magnetic splitting to be followed from the linear Zeeman regime to the incomplete and complete Paschen-Back regimes. The widely used multi-level model in turn assumes only the linear Zeeman regime, resulting in a simpler and more developed formalism. The implementation is checked against analytic results from LL04, the Unno-Rachkovsky solution for local thermodynamic equilibrium (LTE) Zeeman transfer, the Hazel2 He I D3 synthesis, and published self-consistent non-LTE scattering benchmarks. The examples show how the intra-term magnetic mixing produces departures from a linear Zeeman multi-level description, and how a J-constrained multi-term approach can be used to isolate this effect on a chosen fine-structure component. Synthesizing the same spectral line with interchangeable multi-term and multi-level descriptions under identical conditions isolates the signatures of intra-term magnetic mixing and inter-J coherences from the linear Zeeman response. Such controlled comparisons are central to developing scattering polarization diagnostics applicable across multiple atomic descriptions.
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Instrumentation and Methods for Astrophysics

Making Euclid VIS Imaging AI-Ready: A Scalable Pipeline for Morphology, Anomaly Detection, and Similarity Search

The Euclid mission is delivering an unprecedented volume of high-resolution galaxy imaging, posing new challenges for standardized and reproducible reuse across morphological analyses. We present a scalable pipeline that converts released VIS cutouts into standardized $224\times224$ model inputs and uses a pretrained DINOv2 ViT-S/14 feature extractor to construct a 365,513-row, 384-dimensional cutout-and-embedding product from the Galaxy Zoo Euclid (Q1) catalogue. Initial production of the 365,513 released cutouts required approximately 48 hours, corresponding to an estimated end-to-end rate of $2.12$ cutouts s$^{-1}$. The service supports batch task management, while persistent reuse of generated products avoids repeating mosaic extraction for matching requests; together with released-scale production, these mechanisms define the operational scalability considered here. The representation is evaluated with held-out regression, few-label classification, anomaly-candidate prioritization, and similarity retrieval. Held-out ridge probes yield $R^2=0.377$–$0.596$ across four catalogue quantities. Under a one-percent total labelled budget that includes validation, frozen MLP macro-F1 is 0.802–0.861 for three tasks but 0.484 for the strongly imbalanced spiral task; limited final-block fine-tuning gives 0.810–0.850 for those three tasks and 0.520 for spiral. The historical anomaly workflow identifies 1,681 configuration-dependent candidates, and the displayed examples illustrate image-quality failures without estimating their prevalence. These results show that a standardized image interface and a reusable pretrained embedding can support several downstream analyses at the scale of the released Euclid Q1 sample, while the quantitative performance and interpretation remain task dependent under the declared input and evaluation contracts.
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All authors Jinhui Xie, Yunfei Xu, Zhen Zhang, Lang Chen, Chenzhou Cui

High Energy Astrophysical Phenomena

Pulse profiles of tall accretion columns in X-ray pulsars

Accreting X-ray pulsars (XRPs) are strongly magnetized neutron stars (NSs) distinguished by a periodic variability pattern related to the rotation of their magnetospheres (pulsations). Many of these objects show complex asymmetric pulse profiles that are difficult to explain in the framework of existing models. We calculate the pulsations of X-ray radiation from a magnetized NS in the regime of supercritical accretion, when the radiation shock wave is high above the NS surface, and the observed radiation comes from two optically thick accretion columns located downstream of the shocks. We show that the accretion column beam pattern calculated from the first principles has a potential of reproducing the variety of XRP pulse shapes. The surfaces of the columns are assumed to radiate locally as blackbodies with the temperature distribution following the solution of Basko and Sunyaev (1976). The adopted geometry of the field is an inclined dipole. It is taken into account that the two accretion flows above the shocks attenuate and scatter the radiation of the accretion columns. Using the ray-tracing technique, we obtain a vast variety of pulse shapes controlled by the mass accretion rate, magnetic angle, the direction towards the observer, and the parameters that determine the particular set of magnetic field lines being loaded with accreting matter. We propose a universal dimensionless parameter describing the asymmetry of a pulse quantitatively. The model naturally produces asymmetric pulse profiles observed in many XRPs. Its applicability, however, is limited to the brightest objects like pulsating ultraluminous Xray sources and strong flares of Galactic XRPs.
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Earth and Planetary Astrophysics

Pre-accretional irradiation of comet 67P/Churyumov-Gerasimenko constituents

Comets are thought to have largely preserved the primordial material from which they formed. Therefore, cometary studies provide important clues about the processes involved in the formation of the Solar System. During the last weeks of ESA's Rosetta mission, the COSIMA (COmetary Secondary Ion Mass Analyser) instrument performed a series of measurements, which involved long-term sputtering of dust particles captured from comet 67P/Churyumov-Gerasimenko. These post-sputtering analyses revealed the subsurface composition of 8 particles, which we compare here with surfaces composition measured on 59 un-sputtered particle fragments for 9 elements. We found that the analysed surfaces are strongly depleted in metals, such as Mg and Fe, compared to solar abundances, while the subsurface material is consistent with solar values. Because the dust captured by COSIMA fragmented upon impact with the collection targets, this metal depletion cannot reside exclusively on the outer surface of the bulk particles. Instead, these depletion layers must coat the surface of smaller, unfragmented mineral subunits. Such depletion layers, which are often called 'rims', are common at the surface of small regolith dust particles found on airless bodies in our solar system and are attributed to space weathering. We suggest that these mineral cometary subunits experienced pre-accretional solar wind irradiation in the inner regions of the solar nebula during the early stages of Solar System formation. The small irradiated dust constituents must then have been transported to the outer regions of the solar nebula, where they mixed with ices to form the nucleus of the comet.
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All authors Inès Sansberro, Nicolas Fray, Hervé Cottin, Cécile Engrand, Donia Baklouti, Christelle Briois, Anaïs Bardyn, Henning Fischer, Klaus Hornung, John Paquette, Jouni Ryno, Olivier J. Stenzel, Laurent Thirkell, Martin Hilchenbach

High Energy Astrophysical Phenomena

Global Spline Fit: A unified data-driven view of the cosmic-ray spectrum and mass composition from GeV to the highest energies

The energy spectrum and mass composition of cosmic rays are measured by two complementary classes of instruments: space- and balloon-borne detectors that resolve individual elements up to sub-PeV energies, and ground-based air-shower observatories that extend the reach to beyond $10^{11}$ GeV but resolve only broad mass groups. The Global Spline Fit (GSF) is a data-driven model that combines both into a single, self-consistent description of the flux of all elements from hydrogen to nickel. The flux of four leading mass groups is parametrized by cubic basis splines, imposing smoothness but no astrophysical expectation on the spectral shape, while the energy-scale offsets of the participating experiments are cross-calibrated within their quoted systematic uncertainties as part of the fit. The model is defined at the local interstellar spectrum, with the effect of solar modulation at the lowest energies accounted for in the fit. The fit uses the most precise recent data, among them the elemental spectra from AMS-02, CALET, and DAMPE, the knee-region measurements of LHAASO, and the fluorescence-based composition of the Pierre Auger Observatory, and describes about one thousand data points with $\chi^2/\mathrm{ndf}\approx 1.3$, or 0.83 after de-weighting localized disagreements between data sets, demonstrating that the global body of cosmic-ray data is consistent once energy scales are aligned. The model delivers the flux, the mass composition, and their full covariance, along with a compact reduced representation for uncertainty propagation. We further provide the cosmic-ray nucleon flux, which differs from widely used parametrizations by 20-50% over four decades in energy. This exceeds the remaining model uncertainty several times over and has direct consequences for atmospheric neutrino and muon flux predictions.
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All authors Anatoli Fedynitch, Kozo Fujisue, Hans Dembinski, Ralph Engel

Astrophysics of Galaxies

Cool Embeddings: Predicting Galaxy Cluster Cooling Times in IllustrisTNG and TNG-Cluster with AstroCLIP

Foundation models trained on optical astronomical data have not previously been applied to X-ray cluster thermodynamics. We show that embeddings from AstroCLIP, a contrastive vision-language model trained on optical galaxy images and spectra, retain physically meaningful structure when applied to mock Chandra X-ray images of simulated galaxy clusters - a significant shift in observational modality and physical scale. We target the central cooling time ($t_{\mathrm{cool},0}$) of the intracluster medium, a key diagnostic of cluster thermodynamics traditionally requiring X-ray spectroscopy. We present a machine learning framework that predicts $t_{\mathrm{cool},0}$ directly from X-ray images, applied to 711 projections from TNG300 and 993 from TNG-Cluster from the IllustrisTNG simulations. AstroCLIP embeddings form a structured latent space in which clusters with similar thermodynamic properties are naturally grouped, with no equivalent separation by halo mass. Building on this, we introduce a dot-product $k$-nearest neighbour attention model that retrieves similar clusters from the training set and adaptively reweights their cooling times. This model achieves root-mean-square errors of 0.24 (TNG300) and 0.23 (TNG-Cluster) in $\log(t_{\mathrm{cool},0})$, and demonstrates strong out-of-distribution generalisation, outperforming a fine-tuned convolutional neural network trained on raw images (RMSE 0.50 versus 0.73). These results demonstrate that pretrained foundation model embeddings transfer across astrophysical domains and encode thermodynamic information sufficient for inference of cluster cooling properties - offering a scalable path toward cool-core characterisation in all-sky surveys such as eROSITA.
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All authors Rawan Karam, Carter Lee Rhea, Julie Hlavacek-Larrondo, Laurence Perreault-Levasseur, Marine Prunier, Adam Alexandre, Hyunseop Choi

Cosmology and Nongalactic Astrophysics

Bimodal mass primordial black holes in three-field inflation

In this paper, we study the evolution of curvature and entropy perturbations in three-field inflation with non-canonical kinetic terms. Using the kinematic basis in field space, we characterize the background trajectory through its turning rate and non-planar torsion. We also emphasize the inherited structure of perturbations from the kinematic system, which detaches the distinct roles of turning rate and torsion in the interactions among perturbations. We present and study numerically a three-phase model with an intermediate decelerated expansion stage in which two separated transient epochs amplify two distinct families of modes, generating a double-peaked curvature power spectrum. This double-peaked power spectrum leads to the formation of primordial black holes with two characteristic masses, $M_1\sim2\times10^{-12}M_\odot$ and $M_2\sim52M_\odot$ explaining, simultaneously, both dark matter and the LIGO-Virgo-KAGRA binary black hole mass range.
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Cosmology and Nongalactic Astrophysics · Cross-listed from gr-qc

Exact Solutions for Chiral Gravitational Waves from Spin-2 Mixing

A spectator spin-2 field can mix linearly with the metric tensor perturbations. We study the coupled tensor system in an inflationary background, including a parity violating effect parametrised by $\theta$. Without expanding in the linear mixing between the two fields, we solve the system exactly for arbitrary mass while treating the mixing strength nonperturbatively. The mode functions of both helicities are constructed by acting with an operator-valued Gauss hypergeometric function ${}_2F_1$ on Whittaker modes, and the late-time power spectrum of each graviton helicity is expressed in closed form in terms of the generalised hypergeometric function ${}_3F_2$. We find that one helicity is exponentially enhanced, showing that strong mixing with a spectator spin-2 field can generate a large and highly chiral primordial gravitational wave spectrum. The degree of circular polarisation is bounded by $\tanh(\pi\theta)$, independently of the spin-2 mass and the mixing strength. The same solution also gives the late-time power spectrum of the spectator field and its cross spectrum with the graviton. In the weak mixing limit, our exact result reproduces the perturbative Schwinger-Keldysh result. These solutions provide a nonperturbative framework for studying primordial gravitational waves sourced by additional tensor modes.
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Earth and Planetary Astrophysics

Application and Evaluation of the Material Point Method for Low-Velocity Asteroid Collisions Involving Large Deformations

The collisional lifetimes of asteroids larger than $\sim 10$ km in the present-day main belt are estimated to exceed the age of the solar system, suggesting that their shapes may preserve memories of the collisional environment in the primordial solar system. Recent studies performed systematic simulations of equal-mass and low-velocity ($50$–$400\,\mathrm{ms}^{-1}$) collisions between 50-km-radius asteroids using Smoothed Particle Hydrodynamics (SPH), identifying the impact conditions that produce irregular shapes. As an alternative approach, we here employ the Material Point Method (MPM), a particle-grid method well suited to large deformation of solids and free from tensile instability, and we assess its applicability to such systems by direct comparison with the established SPH results. We integrate a previously established rock model combined with a fracture model, the Tillotson equation of state, and Drucker-Prager friction, with the efficient non-associative Drucker-Prager plasticity solver originally developed for granular flows. We perform 135 collision simulations of equal-mass rocky asteroids spanning 15 impact velocities ($50$–$400\,\mathrm{ms}^{-1}$) and 9 impact angles ($5$–$45^\circ$), following the setup of the previous SPH simulations. The mass, axis ratio, and shape classification of the largest remnants closely reproduce the trends of the previous SPH simulations. Since most material transitions into a granular state early in the collision, this agreement appears to depend primarily on the validity of the frictional treatment of the granular material, rather than on the details of the fracture model. These results demonstrate the applicability of MPM to low-velocity asteroid collision simulations and support cross-validation between MPM- and SPH-based approaches.
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Cosmology and Nongalactic Astrophysics

AGN hosting jets. II: Deriving fundamental information from semi-analytical models and the LoTSS sample

Galactic activity has been shown to play a fundamental role in galaxy and cluster evolution throughout the history of the Universe. In the last decades, a number of works have tackled the determination of radio luminosity functions and their evolution, with the aim to understand and quantify this role. In this work we propose a different approach, based on the application of a semi-analytical model to produce mock populations of radio loud active galaxies throughout several orders of magnitude in power, and the comparison with observational samples. The aim of this work is to test the ability of our semi-analytical model to reproduce luminosity and size distributions of large numbers of sources from the radio-loud active galactic nuclei sample from the LoTSS survey. We apply our semi-analytical model for the evolution of radio galaxies and generate hundreds of thousands of sources applying random selection of parameters within probability distributions for each of them. Our results show that the model is able to reproduce the main features of the observed sample, and identifies jet mass-load included in our model and activity periods as critical parameters that should be addressed in more detail in future work. These initial results allow us to establish a maximum activity period ranging from 10 to 200 Myr within an active time distribution probability p(t_max) \propto 1/t_{max}. We also reproduce the radio luminosity function for the z<0.6 population, and the jet power spectrum from 10^{34.5} W to 10^{38} W. Our results show that mass-load is a fundamental parameter in the determination of radio source luminosities with distance, mainly in the low-power regime. Our model predicts that at least 3-4 x 10^{5} radio galaxies must exist in the LoTSS field in order to obtain the 17045 observed ones. This population is vastly dominated by low power sources.
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All authors Pau Beltrán-Palau, Manel Perucho, José-María Martí, Xavier López-López

Solar and Stellar Astrophysics

Multiple regular frequency spacings in $\delta$ Scuti stars from automated analysis of TESS oscillation spectra

The oscillation spectra of rapidly rotating $\delta$ Scuti stars are difficult to interpret because rotation modifies both the frequencies and spatial structure of the modes. Although theoretical studies predict that acoustic modes should organize into approximately equally spaced frequency sequences, systematic searches for such patterns have been limited by the absence of scalable, statistically robust detection methods. We present an automated statistical framework for identifying approximately equally spaced mode sequences in stellar oscillation spectra while quantifying the significance of each candidate detection. We apply this method to oscillation spectra of 4,681 $\delta$ Scuti stars observed by the Transiting Exoplanet Survey Satellite (TESS). The analysis identifies regular mode sequences in a large number of stars and, in many cases, reveals multiple independent regular frequency spacings within the same oscillation spectrum. While the existence of regular sequences is broadly consistent with theoretical expectations for rapidly rotating acoustic modes, the occurrence of multiple dissimilar spacings is not readily explained by current models. Differences in acoustic travel times between known island-mode families appear insufficient to account for the observed diversity of spacings, suggesting that additional mode families or other physical effects contribute to the organization of oscillation spectra of $\delta$ Scuti stars. Our results provide a scalable framework for studying regular mode sequences in large stellar surveys and new observational constraints on oscillations in rapidly rotating stars.
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All authors Shravan M. Hanasoge, Shashwat Chamoli, Subrata Kumar Panda, Daniel R. Reese

Instrumentation and Methods for Astrophysics

GPUPHOT: A Python Framework for High-Performance GPU-Accelerated Photometry and Distributed Astronomical Data Reduction

We present GPUPHOT, an open-source Python framework for GPU-accelerated real-time photometry and astrometry of astronomical CCD and scientific CMOS images. Four of its seven stages run entirely on the GPU through CuPy (background estimation, source detection, PSF modeling and aperture photometry); the catalog crossmatch selects a CPU or GPU backend by problem size, and the zero-point and astrometric calibrations run on the CPU, within a containerized distributed system. Checkpoint-based GPU memory monitoring and an opt-in spatial-binning fallback let a single container image run on GPUs from a 4 GB laptop card to 80 GB datacenter accelerators. We benchmark the framework on nineteen observations from two robotic facilities, the Two-meter Twin Telescope and the Transient Survey Telescope, spanning 4.2 to 151.2 megapixels and 228 to 134,206 cataloged sources, on eight NVIDIA GPU platforms with one process per image. The H100 completes the densest 151.2-megapixel field end-to-end in 31.9 s, and GPU source detection on the A100 is 6-15x faster than the CPU library sep on the same frames. Once three sources of non-determinism are pinned, catalogs and zero points agree to the fourth decimal across GPU models and host CPUs. In this one-process-per-image regime the CuPy 14 / cuML stack showed a 7% lower peak memory and a median 38% higher per-image latency than CuPy 12, both due to the RAPIDS allocator displacing the CuPy memory pool at import; restoring the pool removes the memory difference and cuts the median overhead on datacenter GPUs to 11%, with identical output. Long-lived workers, the production mode, run the two stacks near parity. We recommend the CuPy 14 stack for its reproducibility and maintained libraries, not for memory or speed. GPUPHOT and its benchmark scripts are released for autonomous facilities that require end-to-end photometric reduction at survey cadence.
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All authors Samuel Lemes-Perera, Miguel R. Alarcon, Miquel Serra-Ricart, Pino Caballero-Gil

Cosmology and Nongalactic Astrophysics

Observing population III stars in the pristine region

The detection of the long-sought Population III (Pop III) stars is, perhaps, one of the most intriguing missing links in modern astronomy. Caustic crossing events (CCE) – extreme magnification at the critical curves of galaxy clusters of individual stars at cosmological distances – are postulated to allow for the direct detection of individual Pop III stars. However, in the usual CCE regime, the abundant existence of intracluster stars as microlenses limits the maximum magnification attainable, thus limiting the theoretical detection of luminous stars to relatively low redshifts, significantly smaller than the redshifts where Pop III stars are expected to exist. Here in this letter, we propose to observe Pop III stellar populations as CCEs in the pristine regions of merging clusters. Pristine regions are defined as areas in the lens where the intracluster light, and hence the corresponding stelalr microlenses, is exceptionally low. In thes regions, the low density of microlenses allows background stellar populations to achieve magnification closer to the theoretical limit (whitout microlenses). We show that the maximum magnification in the pristine region scales inversely with the surface mass density of stellar microlenses. Adopting Pop III isochrones, regular James-Webb $\sim29\,$mag observations are sufficient to detect individual Pop III stars in pristine regions, offering a unique observational strategy to detect Pop III stars with the incoming cluster observations. The intermediate regions between high-redshift merging clusters (such as El Gordo) are naturally devoid of microlenses and constitute exceptional targets for the search of Pop III stars.
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High Energy Astrophysical Phenomena

15-Year X-ray Study Links Variable Mass Accretion to Changing Look Behavior in AGN NGC 7582

Changing Look Active Galactic Nuclei (CLAGN) are a subclass of AGN that exhibit spectral state transitions in both optical/UV and X-ray bands on timescales of days to years. In this work, we studied fifteen years of X-ray data of the CLAGN NGC 7582 taken from Suzaku, XMM-Newton, and NuSTAR to understand the origin of the CL behavior. Our study reveals that the obscuration (Hydrogen column density, $N_H$) along the line of sight is associated with the failed wind scenario. The variation in mass accretion is the key that can solely explain the origin of both the failed wind and CL behavior. The mass accretion behavior in NGC 7582 resembles the hard spectral state of black hole binaries. Furthermore, the observed CL timescales in NGC 7582 can be explained either by the dynamical timescale at the BLR or by viscous and thermal timescales at the boundary layer of the corona for a black hole mass of $5.3^{+0.5}_{-0.3} \times 10^7 M_\odot$. Our study thus highlights a direct physical link between the corona and the BLR, which may be potential drivers of the CL behavior.
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All authors Santanu Mondal, V. Jithesh, Neeraj Kumari, Tek P. Adhikari

High Energy Astrophysical Phenomena

Constraints on Supermassive Black Hole Binaries from the Lack of Resolvable Sources in the NANOGrav 15-yr Dataset

Pulsar timing arrays (PTAs) have found evidence of a gravitational wave background (GWB) consistent with a population of supermassive black hole binaries (SMBHBs), but have not yet resolved a continuous wave (CW) from an individual binary. We present the first SMBHB population constraints incorporating PTA upper limits on CWs, based on the NANOGrav 15-year (NG15) data. Using semi-analytic models to generate simulated populations, we calculate each sample's GWB likelihood by free spectral comparison and CW nondetection (nCW) likelihoods by (1) mapping each realization's highest CW signal-to-noise ratio (S/N) to a detection probability and (2) counting the fraction of realizations without a binary close enough that NG15 would have detected it. CW nondetection favors populations in which many lower-mass sources, rather than a few ultramassive ones, dominate the GWB. This information is complementary to that provided by the GWB amplitude, breaking the degeneracy between the masses and number of binaries required to reproduce the observed spectrum. Relative to GWB-only constraints, the joint posteriors favor higher galaxy merger rates, lower $M_\mathrm{BH}$-$M_\mathrm{bulge}$ scatter, shorter binary lifetimes, and steeper small-separation hardening. The most detectable sources in the S/N-weighted joint posterior have chirp masses $\sim 10^{9.6} M_\odot$, luminosity distances $\sim$1300 Mpc, and frequencies $\sim$6 nHz, while the nCW-only constraints favor lower frequencies, coinciding with the NG15 4 nHz candidate. These constraints will tighten if CW nondetection continues.
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All authors Emiko C. Gardiner, Kayhan Gültekin, Philippe Turgeon, Bence Bécsy, Laura Blecha, Nikita Agarwal, Gabriella Agazie, Akash Anumarlapudi, Anne M. Archibald, Zaven Arzoumanian, Anjana Ashok, Jeremy G. Baier, Paul T. Baker, Adam Brazier, Paul R. Brook, Sarah Burke-Spolaor, Rand Burnette, Robin Case, J. Andrew Casey-Clyde, Maria Charisi, Shami Chatterjee, Tyler Cohen, James M. Cordes, Neil J. Cornish, Fronefield Crawford, H. Thankful Cromartie, Kathryn Crowter, Megan E. DeCesar, Paul B. Demorest, Heling Deng, Lankeswar Dey, Timothy Dolch, Graham M. Doskoch, Elizabeth C. Ferrara, William Fiore, Emmanuel Fonseca, Gabriel E. Freedman, Nate Garver-Daniels, Peter A. Gentile, Kyle A. Gersbach, Joseph Glaser, Deborah C. Good, Aiden Gundersen, C. J. Harris, Jeffrey S. Hazboun, Ross J. Jennings, Aaron D. Johnson, Megan L. Jones, David L. Kaplan, Anala Kavumkandathil Sreekumar, Luke Zoltan Kelley, Matthew Kerr, Joey S. Key, Nima Laal, Michael T. Lam, William G. Lamb, Bjorn Larsen, T. Joseph W. Lazio, Natalia Lewandowska, Tingting Liu, Duncan R. Lorimer, Jing Luo, Ryan S. Lynch, Chung-Pei Ma, Dustin R. Madison, Ashley Martsen, Cayenne Matt, Alexander McEwen, James W. McKee, Maura A. McLaughlin, Natasha McMann, Bradley W. Meyers, Patrick M. Meyers, Matthew T. Miles, Chiara M. F. Mingarelli, Andrea Mitridate, Cherry Ng, David J. Nice, Shania A. Nichols, Stella Koch Ocker, Daniel J. Oliver, Ken D. Olum, Timothy T. Pennucci, Benetge B. P. Perera, Polina Petrov, Nihan S. Pol, Henri A. Radovan, Scott M. Ransom, Paul S. Ray, Joseph D. Romano, Jessie C. Runnoe, Alexander Saffer, Shashwat C. Sardesai, Ann Schmiedekamp, Carl Schmiedekamp, Kai Schmitz, Levi Schult, Brent J. Shapiro-Albert, Xavier Siemens, Joseph Simon, Sophia V. Sosa Fiscella, Ingrid H. Stairs, Daniel R. Stinebring, Kevin Stovall, Abhimanyu Susobhanan, Joseph K. Swiggum, Jacob Taylor, Stephen R. Taylor, Mercedes S. Thompson, Jacob E. Turner, Michele Vallisneri, Rutger van Haasteren, Joris P. W. Verbiest, Sarah J. Vigeland, Haley M. Wahl, Kevin P. Wilson, Caitlin A. Witt, David Wright, Olivia Young

Astrophysics of Galaxies

The Physical Origins of Scatter in the Dust Attenuation Scaling Relation of Star-Forming Galaxies: Star–Dust Geometry

Characterising the physical drivers of dust attenuation in star-forming galaxies (SFGs) is essential for interpreting their spectral energy distributions and star formation histories. The infrared excess (IRX$\equiv$$L_{\rm IR}/L_{\rm UV}$) follows a universal scaling relation with metallicity, star formation rate, galaxy size, and inclination. However, the origin of the scatter around this relation remains poorly understood. We revisit this relation using $\sim$32,000 local SFGs from SDSS, GALEX, and WISE, and investigate why some galaxies deviate systematically from the best-fit relation. We find that the deviations are systematically linked to UV luminosity. UV-faint SFGs ($\log(L_{\rm UV}/{\rm L}_\odot)\le 9$) exhibit a median IRX excess of +0.23 dex, while UV-bright SFGs ($\log(L_{\rm UV}/{\rm L}_\odot)\ge 10$) show a median deficit of $-$0.20 dex relative to the relation defined by the dominant UV-intermediate population (86.38 percent of the sample). These offsets are not driven by metallicity, total infrared luminosity, or specific star formation rate. Instead, the deviations are closely linked to systematic differences in star–dust geometry. UV-faint SFGs are compact (median $R_{\rm e} = 2.90$ kpc) and preferentially viewed edge-on (median $b/a = 0.41$), leading to high effective dust column densities along the line of sight. UV-bright SFGs are extended (median $R_{\rm e} = 5.99$ kpc) and preferentially viewed face-on (median $b/a = 0.74$), allowing UV photons to escape efficiently. Galaxies with significant bulge components ($B/T > 0.4$) populate the envelope of the relation, exhibiting larger scatter. We conclude that the scatter in the IRX relation can be largely explained by variations in the three-dimensional star–dust geometry, with UV luminosity acting as an effective tracer of these geometric and physical differences.
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All authors Zongfei Lyu, Xian Zhong Zheng, Zhizheng Pan, Antonios Katsianis, Stijn Wuyts, Haiguang Xu, Pedro Cataldi, Wenhao Liu, Man Qiao, Dong Dong Shi, Yuheng Zhang, Shuang Liu, Run Wen, Chao Yang

Cosmology and Nongalactic Astrophysics

Universality classes of sharp gravitational production of light particles

We establish a classification of the gravitational production of light particles across sharp transitions connecting different asymptotic forms of the scale factor. A family of smooth scale factors with a transition duration $\Delta\eta$ is characterized by its regularity in the sharp-transition limit $\Delta\eta\to 0$, leading to three qualitatively different universality classes: $C^0$, $C^1$, and $C^2$-or-smoother. We find that the $C^0$ class exhibits a quadratic enhancement in the energy density of produced particles, $\rho\propto\Delta\eta^{-2}$, while the $C^1$ class shows a logarithmic enhancement, $\rho\propto\ln(1/\Delta\eta)$. No sharp-transition enhancement occurs for the $C^2$-or-smoother class. Using a specific $C^\infty$ model of the scale factor, we derive the energy density analytically and confirm both the predicted quadratic scaling and its coefficient by numerically solving the mode equation. These results identify the regularity of the scale factor in the sharp limit as the key property controlling the sharp-transition enhancement.
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