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Radio and $γ$-ray emissions in blazars, a subclass of active galactic nuclei (AGNs), provide important insight into their high-energy radiation processes. We studied the relation between radio and $γ$-ray emissions using a large sample of 1687 \textit{Fermi} blazars, based on the Radio Fundamental Catalogue and the latest Third Data Release of the Fourth \textit{Fermi} AGN Catalogue. A clear correlation between radio and $γ$-ray fluxes for both BL Lacertae objects (BL Lacs) and flat-spectrum radio quasars (FSRQs) suggests a synchrotron self-Compton (SSC) contribution to both subclasses. The ratio of $γ$-ray and radio emissions, $γ$-ray loudness ($G_{\rm r}$), is further examined with the $γ$-ray photon index ($Γ_γ$) and the synchrotron peak frequency ($ν_{\rm{peak}}$). An anti-correlation between $G_{\rm r}$ and $Γ_γ$ is explained by the shift of the spectral energy distribution rather than the Compton cooling effect. We found that $G_{\rm r}$ shows a positive dependence on $ν_{\rm{peak}}$ for low-synchrotron-peaked BL Lacs (LBLs) and FSRQs, in line with the SSC-contributed scenario, although additional external Compton contributions may account for the substantial scatter observed in LBLs and FSRQs. In contrast, high-synchrotron-peaked BL Lacs (HBLs) reach the plateau of $G_{\rm r}$ between $\log (ν_{\rm peak}/{\rm Hz}) \simeq15.5-16$, possibly indicating the transition from the Thomson to the Klein--Nishina (KN) regime. Interpreting this feature within a one-zone SSC framework could constrain the magnetic field strength of $-4.14 < \log (B/{\rm G}) < -1.69$ for those HBLs affected by the KN suppression.

Electromagnetic cascades initiated by TeV gamma rays from distant blazars provide one of the cleanest indirect probes of the intergalactic medium and, in particular, of intergalactic magnetic fields. However, their interpretation is not completely clear because of an open theoretical question: the extent to which the electron-positron beams generated in the cascade can lose energy through collective plasma processes. If this occurs before inverse Compton scattering produces secondary gamma rays, then the cascade is quenched. Here we present grplinst, a plugin for the CRPropa framework that models plasma-instability cooling acting on electrons and positrons during propagation. We describe the implementation of several prescriptions proposed in the literature, and present illustrative examples. The code is suitable both for bracketing theoretical uncertainties and for performing systematic studies of how plasma-instability assumptions propagate into gamma-ray observables and inferred intergalactic magnetic-field constraints, which is essential for interpreting current and forthcoming observations by high-energy gamma-ray observatories.

JWST observations of Cassiopeia A have revealed the "Green Monster" (GM), a pockmarked region of shocked circumstellar medium (CSM) characterized by circular holes surrounded by bright rings. The origin of these structures remains debated, with proposed mechanisms including post-shock sculpting by ejecta fingers and pre-shock puncturing by fast-moving knots (FMKs). We investigate the physical viability of the FMK-driven scenario using three-dimensional hydrodynamic simulations of FMKs interacting with a dense circumstellar shell, followed by the passage of the supernova remnant forward shock. By exploring a range of knot properties and shell densities, we compare the resulting hole-ring systems with JWST observations. Primary FMKs reproduce the qualitative morphology of the GM but generally produce hole-ring systems larger than the observed $1^{\prime\prime}-3^{\prime\prime}$ ($\sim0.016-0.048$ pc) structures unless the knots are relatively slow ($\lesssim8000$ km s$^{-1}$) and the shell is dense ($n_{\rm sh}\gtrsim200$ cm$^{-3}$). Moreover, the resulting structures are short-lived, becoming significantly distorted within $30-60$ yr after the forward-shock passage. The GM's diverse hole-ring systems and complex kinematics cannot be attributed to a single idealized scenario, but can be instead explained by the simultaneous action of three mechanisms operating within a structured, heterogeneous CSM. While large cavity relics are carved by early-stage primary FMKs, compact pristine rings are produced by recent "first contact" punctures of secondary knots from fragmented ejecta fingers, and older structures are continuously sculpted by long-term post-shock interactions with large-scale ejecta fingers.

Whether cold dense quantum chromodynamics (QCD) matter undergoes a strong first-order phase transition remains an open question. In nature, neutron stars provide the most direct probe of cold dense QCD matter. Theoretically, chiral effective field theory constrains the equation of state of dense matter near nuclear saturation density, while perturbative QCD calculations constrain it at densities well beyond stable neutron-star interiors. We perform Bayesian inference with nonparametric Gaussian-process equation of state for β-equilibrated neutron-star matter under the assumption with and without a strong first-order phase transition, using the tidal deformability from GW170817; the NICER mass--radius measurements of PSR J0740+6620, PSR J0030+0451, PSR J0437-4715, and PSR J0614-3329; chiral effective field theory; and perturbative QCD. Within this Bayesian inference framework, the model comparison mildly to moderately favors a strong first-order phase transition, with its onset most likely lying above the central density of the most massive neutron star. Such an onset reconciles the stiffness required to support massive neutron stars with the softening favored by perturbative QCD from asymptotically high density.

We construct a unified framework for anisotropic strange quark stars combining de Rham-Gabadadze-Tolley (dRGT)-like massive gravity with dark matter (DM) introduced via extended gravitational decoupling (EGD), in which both metric potentials are deformed by independent functions ξ(r) and h(r). Two DM density profiles are embedded in the decoupled θ-sector: the Einasto spike and the Bose--Einstein condensate (BEC). The baryonic sector is governed by the MIT bag model (quark-matter radial pressure <mml:math><mml:mrow><mml:msubsup><mml:mi>p</mml:mi><mml:mi>q</mml:mi><mml:mi>r</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mrow><mml:mi>∊</mml:mi></mml:mrow><mml:mi>q</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mn>4</mml:mn><mml:mi>B</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>/</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math>), while the pressure anisotropy is parametrized by the Horvat-Ilijic-Marunovic (HIM) prescription applied to the total effective radial pressure <mml:math><mml:msubsup><mml:mi>p</mml:mi><mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mi>f</mml:mi><mml:mi>f</mml:mi></mml:mrow><mml:mi>r</mml:mi></mml:msubsup></mml:math>. We show that the cooperative action of the graviton-mass coupling (m<SUP>2</SUP>c<SUB>1</SUB> &lt; 0) and the DM-induced modification of the effective pressure balance (ρ<SUB>E0</SUB> or <mml:math><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mo>≳</mml:mo><mml:mn>50</mml:mn><mml:mspace></mml:mspace><mml:mrow><mml:mi>MeV</mml:mi><mml:mspace></mml:mspace><mml:msup><mml:mtext>fm</mml:mtext><mml:mrow><mml:mo>-</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math>), together with positive anisotropy (β<SUB>anis</SUB> &gt; 0), drives the maximum mass into the mass-gap window 2.5--5 M<SUB>⊙</SUB>. The predicted GW190814 companion radii (12.3--12.8 km) and the PSR J0740+6620 radii (11.6--12.5 km) are consistent with NICER measurements. We verify the Harrison--Zel'dovich--Novikov stability criterion, the Chandrasekhar condition Γ &gt; 4/3, the Herrera cracking condition <mml:math><mml:mrow><mml:mrow><mml:mo>|</mml:mo></mml:mrow><mml:msubsup><mml:mi>v</mml:mi><mml:mi>t</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mi>r</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mrow><mml:mo>|</mml:mo><mml:mo>&lt;=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mrow></mml:math>, causality (<mml:math><mml:mrow><mml:msubsup><mml:mi>v</mml:mi><mml:mi>r</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mi>t</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo>&lt;=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>) and all dominant energy conditions. We observe that the Buchdahl compactness bound 2M/R &lt; 8/9 employed here is the standard GR result. In the present dRGT-like massive gravity framework, the bound receives corrections that we estimate but do not derive in full generality, confirming physical self-consistency throughout the parameter space.

In this paper, we present the results of a blind survey for compact sources in 138 galaxy clusters from the eFEDS X-ray survey. Of these clusters, 96 are new observations. These targets have X-ray mass estimates and redshifts that formally place them above the thermal Sunyaev-Zel'dovich effect (tSZ) survey limits from the Atacama Cosmology Telescope (ACT, DR5), yet were not detected. Compact sources with apparent locations close to (<104") the center of a galaxy cluster can in-fill the tSZ flux decrement, resulting in tSZ surveys missing clusters. To quantify the number of missing clusters from ACT, we carried out a survey at 90GHz using MUSTANG2 on the Green Bank Telescope and achieved a 5-sigma detection limit of 1mJy in the center of each cluster. We detected 11 discrete sources, which when scaled, is slightly lower than our previous tSZ selected sample, M2-ACT (8.0% vs 9.9%). All had radio counterparts. However, unlike the M2-ACT sample, the sources in X-ray selected clusters were concentrated closer to the cluster centers. When their effect on the measured tSZ signal is taken into account the sources we found would result in 4.5% of clusters being missed by tSZ surveys - a result similar to the estimate in recent ACT results. Most of the 96 clusters in eFEDS but not in ACT are a result of noise and overestimation of mass from X-ray measurements.

High-precision laser interferometers are commonly used to search for signatures of random spacetime fluctuations, in an attempt to understand the fundamental nature of gravity. Conventionally, $SU(2)$ interferometers have been used in such experimental investigations. Motivated by [K. Zheng \textit{et al.}, Photon. Res. \textbf{8}, 1653 (2020)], I assess if there is any advantage to be gained by using an $SU(1,1)$ interferometer instead of the $SU(2)$ interferometer. To this end, I compute the quantum Fisher information for estimating the strength and the correlation length of the spacetime fluctuations, and the corresponding classical Fisher information considering different experimentally relevant measurement schemes, in both types of interferometers. I compare the information metrics corresponding to different parameter regimes that are relevant to both current and possible future experimental setups. This helps me assess if and when the $SU(1,1)$ interferometer offers any advantage over the $SU(2)$ interferometer for estimating either the fluctuation strength or correlation length of the spacetime fluctuations.

Using approximately $5000$ numerical-relativity (NR) simulations spanning mass ratios up to $q=128$ and $1200$ black-hole-perturbation-theory (BHPT) simulations extending to $q=1000$, we present fully analytic models for the remnant properties of quasi-circular binary black hole mergers. The models gwModelRemS (for final mass, final spin, peak luminosity, and recoil kick) and gwModelRemP (for final mass, final spin, and peak luminosity) describe nonprecessing and precessing binaries, respectively. Our approach combines analytic insights from post-Newtonian theory and point-particle limits with a data-driven fitting framework which also includes validation-guided AI-agent-assisted optimization. The resulting fits outperform existing analytic models and achieve accuracies comparable to data-driven models within their domains of validity. We also construct gwModelRemP\_flow, a normalizing-flow model for recoil kicks from precessing binaries, marginalized over the in-plane spin orientations. This model additionally utilizes an enlarged low-fidelity training set, beyond the available NR and BHPT simulations, constructed through a waveform-based data-augmentation procedure. We also include simple eccentric extensions through leading-order dependence on eccentricity and orbital anomaly. The models span the equal-mass to extreme-mass-ratio regimes and are publicly available through the gwModels package for applications in gravitational-wave astronomy, astrophysical population studies, and cosmology.

CU Vir, a magnetic hot star, is the first discovered Main-sequence Radio Pulse emitter (MRP) characterized by its ability to produce periodic radio pulses via electron cyclotron maser emission. Although significant advancements have been made in understanding MRPs, their temporal properties remain mostly unexplored. To overcome this limitation, we conducted a pilot study with the Australia Telescope Compact Array, in which we observed pulses from CU Vir at 36 epochs over $1-3$ GHz. In this frequency range, CU Vir produces two $\approx 100\%$ circularly polarized pulses, called `leading' and `trailing' pulses per rotation period. We find significant differences in the variability indices exhibited by the two pulses as a function of frequencies, with the leading pulse showing higher variability throughout our observing band. This result could be explained in the scenario of centrifugal breakout events in the magnetosphere of an oblique rotator causing correlated fluctuations across frequencies, along with intrinsic instabilities associated with coherent emission. In addition, we discover jittering in the arrival phases of pulses that must be considered in future monitoring campaigns. The pulses also exhibit a systematic shift to later arrival times during the course of our observing campaign, allowing us to refine the rotation period to $0.5206882$ days. Finally, we estimate that $\sim 30$ pulses will be needed to extract global pulse properties for the leading or trailing pulses. This relatively small number strongly motivates more extensive monitoring campaigns of MRPs, both to validate our results, and also to pinpoint the origin of the observed temporal variations.

Can gravitational waves probe the near-horizon geometry of black holes, and if yes, which frequency scale is optimal? Although shorter wavelengths usually resolve smaller scales, we show that black-hole scattering may impose an information-theoretic optimum. We study a controlled scattering Gedankenexperiment in which Gaussian pulses of scalar test fields are sent toward a black- hole potential and the reflected waveform is used to infer the geometry. Near-horizon deviations are parametrized with the Rezzolla-Zhidenko metric, and information recovery is quantified by the Fisher matrix in the high-signal-to-noise limit. Narrow, high-frequency pulses resolve short scales but are mostly transmitted through the barrier, while wide pulses are efficiently reflected but poorly resolve the potential. Their competition selects an optimal pulse width, numerically found to be set by about the inverse square root of the potential peak. Using the Pöschl-Teller analytical solutions, we further model the correct excitation of quasinormal modes and separate the information in the fundamental mode from that in the full waveform, including the prompt response. The optimal probe is therefore not the highest-frequency pulse, but the waveform that balances spatial resolution against reflected information, linking black-hole spectroscopy, semiclassical barrier scattering, and information theory.

Reverberation mapping of active galactic nuclei provides one of the most direct probes of the geometry and kinematics of the broad-line region by measuring time delays between continuum and line variability. Modern RM surveys frequently suffer difficulties with lag measurements due to poor signal to noise and aliasing, whereby multimodal lag posterior distributions arise due to seasonal gaps in our data. These challenge the reliability of commonly used fitting tools such as JAVELIN, which can return a high rate of false positives. We implement a new lag measurement package, LITMUS, and introduce a new framework that uses Bayesian evidence to identify false positive lag measurements, as well as examine the question of how many AGN present detectable lags in high redshift industrial scale surveys like OzDES and SDSS. Our analysis differs from previous RM studies in six key respects: (i) our inference is robust to the previously under-diagnosed numerical component of aliasing, (ii) we use a consistent methodology for all sources, (iii) uncertainty in the underlying AGN variability is fully marginalised, (iv) lag significance is assessed via Bayesian model comparison rather than heuristic metrics, (v) false-positive rates are quantified by comparison against random-chance recoveries and (vi) we use marginal likelihoods to distinguish between sources where a lag is not detectable in our data and sources that show no evidence of reverberation. Applied to the OzDES sample, we find that previous RM studies are likely to have overestimated the confidence of recovered lags, and we find a stark contrast between a low reverberation percentage for the MgII line (3-28% depending on assumptions) and much higher percentages in the CIV and especially the H$β$ line, which is consistent with 100%. We also present a re-analysed set of lags from the OzDES sample with better quantified reliabilities

The tracking condition $\dotφ^2=γH^{-m}$ for single scalar field theory leads to analytic inflationary solutions, which are compatible with the current cosmic microwave background radiation experiments. To our knowledge this is the only analytic solution of inflation which is compatible with the data, to date. In this work we seek for some theoretical basis that can lead to the tracking condition $\dotφ^2=γH^{-m}$. As we show, if the Universe is seen pre-inflationary as a quantum statistical system, the scalar field may emerge as a collective condensate of the quantum degrees of freedom. In the quantum-to-classical transition of the Universe, the scalar field two point function yields the susceptibility of the theory with an inherent correlation length. Using information theoretic motivation and Wilsonian quantum field theoretic arguments, we demonstrate that the tracking conditions $\dotφ^2=γH^{-m}$ emerge from this framework.

We investigate how thermodynamic phase transitions are reflected in the quasinormal modes (QNMs) of charged anti-de Sitter (AdS) black holes surrounded by perfect fluid dark matter (PFDM). In the extended phase space, increasing the positive PFDM parameter raises the critical temperature and pressure while reducing the critical horizon radius. We compute the fundamental QNMs of a massless scalar perturbation using a Chebyshev pseudospectral method and analyze their evolution along isobaric and isothermal processes below the critical point. The small and large black hole branches trace clearly separated QNM trajectories and display sharply different slopes near the first-order transition, providing a dynamical signature of the branch change. Along isotherms, this evolution results from the competing effects of the horizon radius and pressure, or equivalently the AdS radius, rather than from the horizon radius alone. At the critical point, however, the QNM frequencies vary smoothly with the horizon radius and show no sharp signature of the second-order transition. Along the coexistence curve, the separation between the small and large black hole QNMs decreases as the Gibbs free energy swallowtail shrinks and vanishes at criticality. These results show that PFDM shifts both the thermodynamic phase structure and the associated QNM response, while the fundamental scalar QNM spectrum remains sensitive to the first-order small/large black hole transition.

We introduce a density-level pivot construction for the Chevallier-Polarski-Linder (CPL) parameterization by defining the normalized dark energy density $f_p\equiv f_{\rm DE}(a_p)$ and the equation of state $ω_p\equiv ω(a_p)$ at an optimized pivot scale factor $a_p$. This reparameterization leaves the underlying CPL cosmology unchanged and allows the two models to be compared using parameters with a direct physical interpretation at the epoch where the data are most sensitive. Accordingly, following the DESI DR2 results, we compare a newly proposed $f_a f_b$CDM parameterization, based on a second-order Taylor expansion of the normalized dark energy density, with the standard $w_0w_a$CDM model. In particular, we constrain the original and pivoted parameterizations using compressed cosmic microwave background (CMB), DESI DR2 baryon acoustic oscillations (BAO), cosmic chronometers (CC), and Pantheon+ Type Ia supernovae data, with the SH0ES prior imposed on $H_0$. We find that applying the same density-level pivot prescription to the $w_0w_a$CDM model substantially reduces the correlation between its dark energy parameters and provides tighter and more stable constraints. The statistical comparison shows that this model remains favored over the Taylor expansion of the dark energy density, even when both models are analyzed in the optimized parameter basis. Moreover, the pivoted CPL parameterization accurately reproduces the background evolution of quintessence models, providing a reliable phenomenological approximation to the underlying dark energy dynamics, better than the $f_af_b$CDM model. We conclude that changing the parameter basis improves the performance of the $w_0w_a$CDM model, which emerges as the most suitable framework to describe the dark energy sector within the class of models considered here.

Gravitational lensing is often introduced through the bending of light by mass, but its geometrical nature can be difficult to visualize without invoking the full machinery of general relativity. We present a geometrical-optics analogy in which selected lensing-like image morphologies are generated by ray tracing through axicon-type lenses. In contrast with analogies based on a spatially varying refractive index, the present model uses optical elements with a constant refractive index; the redistribution of rays is produced by the geometry of the refracting surfaces. After deriving the ray-tracing equations for a general two-surface axicon, we apply the model to conical and exponential profiles. Axially symmetric configurations generate ring-like images, misaligned incidence produces partial arcs, and broken axial symmetry leads to four-image patterns reminiscent of an Einstein cross. The model is not intended as a physical substitute for a relativistic lens equation, but as a computational and pedagogical tool for exploring how surface geometry and symmetry control ray deflection, redistribution, and image multiplicity.

We investigate how sub-sonic compressible magnetohydrodynamic (MHD) turbulence properties that are relevant for cosmic-ray (CR) transport in the Galaxy are affected by the nature and amplitude of initial fluctuations, and by the plasma compressibility $β$. We perform 3D simulations of decaying compressible ideal-MHD turbulence at $1024^3$ resolution with the PLUTO code. The level of density fluctuations in fully developed turbulence is insensitive to whether this state is reached starting from Alfvénic or fast-magnetosonic perturbations. Fast-magnetosonic injection is characterized by an early phase of rapid shock dissipation, followed by a turbulence-dominated decay with a rate comparable to that of the Alfvénic case. The contribution of fast-magnetosonic fluctuations in fully developed turbulence remains relevant only when the initial injection consists exclusively of fast modes. Large-amplitude turbulence ($δB/B_0>1$) is characterized by a nearly isotropic Kolmogorov or Iroshnikov-Kraichnan spectrum for Alfvénic or fast-magnetosonic injection, respectively. At low amplitudes ($δB/B_0\ll1$), both initial Alfvénic and mixed-wave perturbations lead to strongly anisotropic turbulence with spectra $\propto k_\perp^{-5/3}$ and $\propto k_z^{-2}$ (becoming steeper at $β\gg1$), whereas fast-magnetosonic perturbations produce a turbulent state populated by shocks with a nearly isotropic $k^{-2}$ spectrum. Magnetic-field curvature and mirror structures are strongly sensitive to fluctuation amplitude and plasma $β$. The predicted -2.5 power-law scaling emerges only in the large-amplitude regime at high $β$. This work highlights that features of sub-sonic compressible MHD turbulence that may affect CR transport are sensitive to large-scale conditions and to the plasma $β$. Their effect on CR diffusion and field-line random walk is the object of Paper II.

We investigate how nonmetricity affects particle creation and evaporation in rotating bumblebee black holes by comparing metric and metric-affine solutions. We normalize the stationary Killing vectors at spatial infinity before defining physical frequencies, angular velocities, and temperatures. This procedure changes the static comparison and gives the leading calibration $\ell=3X/4$. In the metric solution, $\ell$ shifts the horizons, stationary limit surfaces, and extremal boundary, increases the normalized horizon angular velocity, and suppresses the Hawking temperature. Nevertheless, the surface gravity remains uniform and the scalar wave equation separable. We derive the tunneling factors, quantum occupation numbers, radial potential, and an analytical lower bound for the axisymmetric greybody factor. In the metric-affine geometry, nonmetricity preserves the Kerr coordinate locations of the horizons and stationary limit surfaces, but changes the physical horizon area, normalized angular velocity, and meridional sector. The component $g_{rθ}$ couples angular channels, whereas the local surface gravity depends on latitude when $aX\neq0$. Consequently, the generic rotating configuration admits neither a single global Hawking temperature nor an independent channel-by-channel emission spectrum. In the static limit, under the same Stefan-Boltzmann prescription, both Lorentz-violating geometries have lower luminosities and longer lifetimes, with the metric-affine black hole radiating less and evaporating more slowly. A local slow-rotation expansion preserves this tendency but does not establish a global rotating evaporation hierarchy. Existing weak-field constraints limit fractional corrections to static quantum-emission observables to below $1.3\times10^{-11}$.

We have investigated effects of Lorentz violation (LV) on bright ring in Sgr A* images illuminated by the 230 GHz thermal synchrotron emission from radiation ineffective accretion flows around a rotating LV black hole within the low-energy Hořava gravity framework. Our results reveal that the LV parameter reduces the bright ring diameter yet increases its width, luminosity, azimuthal asymmetry and orientation angle. Higher spin parameter strengthens the LV-induced effects on bright ring properties.Increasing disk thickness reduces the ring diameter and enhances the LV parameter's effects on this diameter. The ring width shows no systematic dependence on the disk thickness. These quantities of bright ring display similar trends against black hole spin and the LV parameter for the rotating LV black hole. Using EHT observational data of Sgr A*, we find that, at fixed disk thickness, the allowed range of the LV parameter first broadens and then contracts with growing black hole spin, and shifts toward smaller LV parameter values. In addition, the LV parameter narrows the permitted range of black hole spin: negative LV parameter values shift this range to higher spin, while positive values shift it to lower spin. Finally, we probe effects of the LV parameter on the peak position value and the width of the primary image and the $n=1$ photon ring for the rotating LV black hole. The peak positions and their widths decrease with the LV parameter, except for a narrow range. The peak position differences for various LV parameter are more pronounced for pure Keplerian accretion flow. In additional, the primary image and the $n=1$ photon ring produced by pure radially free-falling flows are broader than their counterparts generated by pure Keplerian flows.

We investigate the Emden-Fowler equation $u''=-x^ru^p, u(0)=1, u'(0)=0$, with roots in astrophysics, and study the qualitative and quantitative dependence of its solution on the parameters; the analytical work is paralleled by numerical simulations. A special attention is given to estimating the first zero $x_0$ of $u$ in terms of $r, p$. The results are used to address two apparently new issues: first, we solve EF backwards starting from $x_0$; second, we transform it into an overdetermined boundary value problem and decide when is this solvable.

We present the science motivation, preliminary design requirements, device laboratory testing and a prototype for an new experimental platform for solar observations, MiraSOL. MiraSOL will use digital micromirror technology to actively select regions on the solar disk for spectroscopic observation to determine the spatially dependent radial velocity signatures of stellar variability, and can create transits on the solar disk to probe the effects of stellar contamination on exoplanet transmission spectra. MiraSOL uses the Texas Instruments DLP801RE as a spatial light modulator to allow a mask, with 3 arcsecond spatial sampling per micromirror, capable of resolving features on the solar disk. This instrument will have a fiber output which can then be coupled with state-of-the-art extreme precision radial velocity (EPRV) spectrometers, such as HPF or NEID, for high resolving power, stable spectra of sunspots and plage, or a low resolution spectrometer for studies of stellar contamination in transit spectra. We discuss a 60 Hz flicker signal we discovered, likely due to the commercial off-the-shelf (COTS) evaluation board of the digital micromirror device electronics. We also build a proof-of-concept prototype and demonstrate imaging and pixel-level control of the full solar disk to demonstrate the feasibility of this technology.

We report the first detection of TiO in star-forming regions based on Atacama Large Millimeter/submillimeter Array observations of Orion Source I, a well-characterized massive protostar. Multiple rotational transitions are identified, with emission spatially resolved within $\sim 50$ au, showing a compact distribution with a velocity structure consistent with the base of a rotating outflow. The spatial and velocity distributions of TiO are consistent with those of AlO, with both species being key dust seeding refractory molecules. \textbf{The column density of TiO is derived to be $(3.0 \pm 0.4)\times10^{15}\ {\rm cm^{-2}}$, corresponding to $X_{\rm TiO/SiO} \sim 12.8 \pm 1.7 \times10^{-3}$, higher than CI chondrites and indicative of efficient dust-to-gas conversion near the protostar.} We also identify a tentative detection of AlOH, which exhibits a more extended distribution along the disk surface, possibly indicating different conditions from those traced by TiO and AlO. The detection of TiO, a key dust seeding species, offers important constraints on refractory chemistry and the formation environments of primitive minerals, linking astrochemical processes in protostellar systems to the earliest stages of Solar System material formation.

We study the linearised spin-2 field on conformally compactified Minkowski spacetime. Initial data are prescribed on past null infinity $\mathscr{I}^-$, and the system is evolved through the cylinder at spatial infinity to future null infinity $\mathscr{I}^+$. To avoid the development of logarithmic singularities and thereby preserve smooth peeling behaviour, we derive explicit conditions on the freely specifiable ingoing gravitational radiation $ψ_0$ at $\mathscr{I}^-$ that ensure regular initial data. For compactly supported data, we obtain necessary and sufficient integral conditions guaranteeing regularity and compact support of the full system. In the simplest cases, we construct examples of exact initial data, while for the general case, we present a numerical procedure that computes the remaining $ψ_k$ to obtain a full initial data set. We perform numerical evolutions using two gauges corresponding to compactification of either a neighbourhood of spatial infinity or the entire Minkowski spacetime, and demonstrate stable propagation of the system from $\mathscr{I}^-$ to $\mathscr{I}^+$. These results provide a step towards a framework for fully global simulations of gravitational radiation and clarify the role of initial data on $\mathscr{I}^-$ in determining asymptotic structure.

Using the thermodynamic approach introduced in e-Print: 2206.09124 [hep-th] to the case of Kerr-NUT solution, we demonstrate the existence of a new conserved quantity that is dual to the angular momentum, in the same way that the nut charge "n" is dual to the mass "m". This quantity exists regardless of the presence of the Kerr rotation parameter $a$, but only affects its thermodynamics when $a\neq 0$. The thermodynamic quantities calculated together with the two charges $N_{c}=cn$ and $n$ lead to consistent thermodynamic relations. That is, the first law, Smarr's and Gibbs-Duhem relations are all satisfied.