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The X9.3 solar flare on 6 September 2017 was the most intense of Solar Cycle 24. Based on the in situ observations from the Swarm constellation and simulations from the Thermosphere-Ionosphere-Electrodynamics General Circulation Model, this work explored the three-dimensional evolution of the equatorial ionization anomaly due to the X9.3 flare. The altitudinal disturbances in the noon electron density (Ne) exhibited a "butterfly-shaped" pattern. In the lower ionosphere (&lt;280 km), Ne was enhanced at all latitudes, with relative/absolute increases of up to ∼40%/1.30 × 10<SUP>11</SUP> m<SUP>−3</SUP>. The chemical production contribution was strongest near the lower boundary (∼200 km, peaking at 2.13 × 10<SUP>11</SUP> m<SUP>−3</SUP>) and decreased progressively with altitude to less than 10<SUP>9</SUP> m<SUP>−3</SUP> at ∼550 km. The flare-induced westward electric field drove downward E × B drifts (peaking at −3.84 m/s), resulting in bottomside Ne enhancement (1.92 × 10<SUP>10</SUP> m<SUP>−3</SUP>) and localized topside depletion (−6.79 × 10<SUP>9</SUP> m<SUP>−3</SUP>) via a reverse fountain tendency. The enhanced Ne also exhibited hemispheric asymmetry at 300 km, being stronger in the northern hemisphere (1.10 × 10<SUP>11</SUP> m<SUP>−3</SUP> at 16.78° MLat, 30° geographic longitude (GLon)) than in the southern hemisphere (8.30 × 10<SUP>10</SUP> m<SUP>−3</SUP> at −24.61° MLat, 22.5° GLon). This asymmetry was dominated by plasma transport via neutral winds (17.7%) and ambipolar diffusion (82.3%).

The effective-one-body (EOB) formalism accurately describes the conservative dynamics of general binary orbits, but current implementations of radiation reaction remain largely limited to quasi-circular inspirals. Extending EOB to eccentric orbits currently requires the corresponding post-Newtonian (PN) energy fluxes in EOB coordinates, which are only known to 1PN order. In this paper, we compute the instantaneous gravitational-wave energy flux in EOB coordinates to 2PN accuracy using a systematic coordinate transformation between the Arnowitt─Deser─Misner (ADM) and EOB phase-space variables. We derive the 2PN-accurate transformation laws for the relative coordinates and velocities between the two coordinate systems and re-express the 2PN instantaneous energy flux entirely in EOB variables. Working within the EOB test-particle framework (with finite mass ratio <inline-formula><mml:math><mml:semantics><mml:mi>ν</mml:mi></mml:semantics></mml:math></inline-formula>) for an equatorial elliptic orbit, we adopt a Keplerian reparameterization in terms of the semilatus rectum p, eccentricity e, and two phase variables <inline-formula><mml:math><mml:semantics><mml:mrow><mml:mo>(</mml:mo><mml:mi>ξ</mml:mi><mml:mo>,</mml:mo><mml:mi>ϕ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:semantics></mml:math></inline-formula> associated with the radial and azimuthal motion, which makes the calculations more transparent and facilitates the subsequent computation of gravitational waveforms. Using the conservative orbital angular frequency, we compute the orbit-averaged energy flux. In addition to the energy flux, we also compute the corresponding 2PN angular momentum flux in EOB coordinates using the same transformation method. Our results, expressed in gauge-invariant variables <inline-formula><mml:math><mml:semantics><mml:mrow><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>M</mml:mi><mml:mi>ω</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>/</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:semantics></mml:math></inline-formula> and eccentricity <inline-formula><mml:math><mml:semantics><mml:msub><mml:mi>e</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:semantics></mml:math></inline-formula>, agree with known PN results and show improved accuracy compared to the 1PN EOB fluxes of Hinderer and Babak.

The goal of this paper is to compare the Wheeler-DeWitt approach, understood in a broad sense, with an alternative one, the so-called extended phase space approach to quantization of gravity. By "the Wheeler-DeWitt approach", I mean not only quantum geometrodynamics formulated by DeWitt in his seminal paper of 1967, but also any approach to quantization of gravity based on the Wheeler-DeWitt equation in some form. Since the Wheeler-DeWitt equation is a direct consequence of the Dirac formalism, its analysis requires examination of the latter and its application to gravity. In particular, I argue that there is a contradiction between canonical quantization and the idea put forward by founders of quantum gravity that, in this theory, all possible spacetime topologies should be taken into account. The path integral approach seems to be more adequate then the canonical approach. However, to derive the Wheeler-DeWitt equation from the path integral, most authors make the assumption about asymptotic states, that again contradicts the supposition of arbitrary spacetime topology. The extended phase space formalism is entirely based on the path integral approach. Note that if one refuses the assumption about asymptotic states, one cannot prove the gauge invariance of the path integral, and the Wheeler-DeWitt equation loses its sense. In the alternative approach, one derives the Schrodinger equation instead. Thus, the extended phase space approach is really beyond the Wheeler-DeWitt approach. The features of this alternative approach are explored with special emphasis on conclusions that cannot be obtained by using the Wheeler-DeWitt quantum geometrodynamics.

Semianalytic models are a widely used approach to simulate galaxy properties within a cosmological framework, relying on simplified yet physically motivated prescriptions. They have also proven to be an efficient alternative for generating accurate galaxy catalogs, offering a faster and less computationally expensive option compared to full hydrodynamical simulations. In this paper, we demonstrate that, using only galaxy 3D positions and radial velocities, we can train a graph neural network coupled to a moment neural network to obtain a robust machine-learning-based model capable of estimating the matter density parameters, Ω<SUB>m</SUB>, with a precision of approximately 10%. The network is trained on (25 h<SUP>−1</SUP> Mpc)<SUP>3</SUP> volumes of galaxy catalogs from L-Galaxies and can successfully extrapolate its predictions to other semianalytic models (GAEA, SC-SAM, and SHARK) and, more remarkably, to hydrodynamical simulations (Astrid, SIMBA, IllustrisTNG, and SWIFT-EAGLE). Our results show that the network is robust to variations in astrophysical and subgrid physics, cosmological and astrophysical parameters, and the different halo-profile treatments used across simulations. This suggests that the physical relationships encoded in the phase space of semianalytic models are largely independent of their specific physical prescriptions, reinforcing their potential as tools for the generation of realistic mock catalogs for cosmological parameter inference.

Observations show that stellar coronal mass ejection (CME) candidates display relatively lower kinetic energies compared to expectations from solar flare─CME relations extrapolated to the stellar regime. This behavior was predicted by studies of magnetic confinement of CMEs by strong large-scale stellar magnetic fields. However, the possible promoting role of stronger small-scale magnetic fields has not yet been properly explored in previous studies. In this work, we present the first parametric study that simultaneously incorporates both the promoting and confining effects of magnetic field strength on CME dynamics. We perform CME simulations with scaled solar magnetograms spanning &lt;B<SUB>⋆</SUB>&gt; = 1, 5, 10, 50, 100 B<SUB>⊙</SUB> and inserting flux ropes whose magnetic energy is set to scale as <inline-formula> <mml:math><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>FR</mml:mi></mml:mrow></mml:msub><mml:mo>∝</mml:mo><mml:msup><mml:mrow><mml:mo>&lt;</mml:mo><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mo>⋆</mml:mo></mml:mrow></mml:msub><mml:mo>&gt;</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> </inline-formula>. Our results show that CME speed and mass increase with magnetic field strength in this restrictive scenario, approximately following v<SUB>CME</SUB> ∝ &lt;B<SUB>⋆</SUB>&gt; and <inline-formula> <mml:math><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mi>CME</mml:mi></mml:mrow></mml:msub><mml:mo>∝</mml:mo><mml:msup><mml:mrow><mml:mo>&lt;</mml:mo><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mo>⋆</mml:mo></mml:mrow></mml:msub><mml:mo>&gt;</mml:mo></mml:mrow><mml:mrow><mml:mn>1.5</mml:mn></mml:mrow></mml:msup></mml:math> </inline-formula>. These trends indicate that, within this idealized solar-scaled framework, increasing the magnetic field strength enhances the net promoting forces relative to the confining forces and drives faster, more massive CMEs. We further identify the upward Lorentz force as the dominant contributor to the acceleration and the mass enhancement. We also conducted additional cases with different flux rope energies that do not follow the above scaling assumption and found that stronger flux ropes produce faster and more massive CMEs for each given stellar model. The adopted scaling assumptions are intended as a controlled parametric experiment rather than a realistic model of young solar-type stars, and future work using more realistic stellar magnetic maps will be required to determine which regions of the parameter space explored here are most relevant to active stars.