Search

Constraining the formation processes of small solar system bodies is crucial for gaining insights into planetesimal formation. Their bulk densities, determined by their compressive strengths, offer valuable information about their formation history. In this paper, we utilize a formulation of the compressive strength of dust aggregates obtained from dust N -body simulations to establish the relation between the bulk density and diameter. We find that this relation can be effectively approximated by a polytrope with an index of 0.5, coupled with a formulation of the compressive strength of dust aggregates. The lowest-density trans-Neptunian objects (TNOs) and main-belt asteroids (MBAs) are well reproduced by dust aggregates composed of 0.1 μ m sized grains. However, most TNOs, MBAs, comets, and near-Earth asteroids (NEAs) exhibit higher densities, suggesting the influence of compaction mechanisms such as collision, dust grain disruption, sintering, or melting, leading to further growth. We speculate that there are two potential formation paths for small solar system bodies. One involves the direct coagulation of primordial dust grains, resulting in the formation of first-generation planetesimals, including the lowest-density TNOs, MBAs, and the parent bodies of comets and NEAs. In this case, comets and NEAs are fragments or rubble piles of first-generation planetesimals, and the objects themselves or the rubble are composed of 0.1 μ m sized grains. The other path involves the further potential fragmentation of first-generation planetesimals into the compact dust aggregates observed in protoplanetary disks, resulting in the formation of second-generation planetesimals composed of compact dust aggregates, which may contribute to explaining another formation process of comets and NEAs. [ABSTRACT FROM AUTHOR]

Accretion disks around both stellar-mass and supermassive black holes (BHs) are likely often warped. Whenever a disk is warped, its scale height varies with azimuth. Sufficiently strong warps cause extreme compressions of the scale height, which fluid parcels “bounce” off of twice per orbit to high latitudes. We study the dynamics of strong warps using (i) the nearly analytic “ring theory” of Fairbairn & Ogilvie, which we generalize to the Kerr metric, and (ii) three-dimensional general-relativistic hydrodynamic simulations of tori (“rings”) around BHs, using the H-AMR code. We initialize a ring with a warp and study its evolution on tens of orbital periods. The simulations agree excellently with the ring theory until the warp amplitude, ψ , reaches a critical value ψ _c . When ψ > ψ _c , the rings enter the bouncing regime. We analytically derive (and numerically validate) that ${\psi }_{{\rm{c}}}\approx {(r/{r}_{{\rm{g}}})}^{-1/2}$ in the non-Keplerian regime, where r _g = GM / c ^2 is the gravitational radius, and M is the mass of the central object. Whenever the scale height bounces, the vertical velocity becomes supersonic, leading to “nozzle shocks” as gas collides at the scale height minima. Nozzle shocks damp the warp within ≈10–20 orbits, which is not captured by the ring theory. Nozzle shock dissipation leads to inflow timescales 1–2 orders of magnitude shorter than unwarped α disks, which may result in rapid variability, such as in changing-look active galactic nuclei or in the soft state of X-ray binaries. We propose that steady disks with strong warps may self-regulate to have amplitudes near ψ _c .

Observations and theory suggest that core-collapse supernovae can span a range of explosion energies, and when sub-energetic the shockwave initiating the explosion can decelerate to speeds comparable to the escape speed of the progenitor. In these cases, gravity will complicate the explosion hydrodynamics and conceivably cause the shock to stall at large radii within the progenitor star. To understand these unique properties of weak explosions, we develop a perturbative approach for modeling the propagation of an initially strong shock into a time-steady, infalling medium in the gravitational field of a compact object. This method writes the shock position and the post-shock velocity, density, and pressure as series solutions in the (time-dependent) ratio of the freefall speed to the shock speed, and predicts that the shock stalls within the progenitor if the explosion energy is below a critical value. We show that our model agrees very well with hydrodynamic simulations, and accurately predicts (for example) the time-dependent shock position and velocity and the radius at which the shock stalls. Our results have implications for black hole formation and the newly detected class of fast X-ray transients (FXTs). In particular, we propose that a "phantom shock breakout"—where the outer edge of the star falls through a stalled shock—can yield a burst of X-rays without a subsequent optical/UV signature, similar to FXTs. This model predicts the rise time of the X-ray burst, t d, and the mean photon energy, kT, are anticorrelated, approximately as T ∝ t d − 5 / 8 . [ABSTRACT FROM AUTHOR]

We introduce “Class Symbolic Regression” (Class SR), the first framework for automatically finding a single analytical functional form that accurately fits multiple data sets—each realization being governed by its own (possibly) unique set of fitting parameters. This hierarchical framework leverages the common constraint that all the members of a single class of physical phenomena follow a common governing law. Our approach extends the capabilities of our earlier Physical Symbolic Optimization (Φ-SO) framework for symbolic regression, which integrates dimensional analysis constraints and deep reinforcement learning for unsupervised symbolic analytical function discovery from data. Additionally, we introduce the first Class SR benchmark, comprising a series of synthetic physical challenges specifically designed to evaluate such algorithms. We demonstrate the efficacy of our novel approach by applying it to these benchmark challenges and showcase its practical utility for astrophysics by successfully extracting an analytic galaxy potential from a set of simulated orbits approximating stellar streams.

Astrophysical explosions that contain dense and ram-pressure-dominated ejecta evolve through an interaction phase, during which a forward shock (FS), contact discontinuity (CD), and reverse shock (RS) form and expand with time. We describe new self-similar solutions that apply to this phase and are most accurate in the limit that the ejecta density is large compared to the ambient density. These solutions predict that the FS, CD, and RS expand at different rates in time and not as single temporal power laws, are valid for explosions driven by steady winds and homologously expanding ejecta, and exist when the ambient density profile is a power law with a power-law index shallower than ∼3 (specifically when the FS does not accelerate). We find excellent agreement between the predictions of these solutions and hydrodynamical simulations, both for the temporal behavior of the discontinuities and for the variation of the fluid quantities. The self-similar solutions are applicable to a wide range of astrophysical phenomena and—although the details are described in future work—can be generalized to incorporate relativistic speeds with arbitrary Lorentz factors. We suggest that these solutions accurately interpolate between the initial “coasting” phase of the explosion and the later, energy-conserving phase (or, if the ejecta is homologous and the density profile is sufficiently steep, the self-similar phase described in R. A. Chevalier).

Compressive strength is a key to understanding the internal structure of dust aggregates in protoplanetary disks and their resultant bodies, such as comets and asteroids in the solar system. Previous work has modeled the compressive strength of highly porous dust aggregates with volume filling factors lower than 0.1. However, a comprehensive understanding of the compressive strength from low (<0.1) to high (>0.1) volume filling factors is lacking. In this paper, we investigate the compressive strength of dust aggregates by using aggregate compression simulations resolving constituent grains based on Johnson-Kendall-Roberts theory to formulate the compressive strength comprehensively. We perform a series of numerical simulations with moving periodic boundaries mimicking the compression behavior. As a result, we find that the compressive strength becomes sharply harder when the volume filling factor exceeds 0.1. We succeed in formulating the compressive strength comprehensively by taking into account the rolling motion of aggregates for low volume filling factors and the closest packing of aggregates for high volume filling factors. We also find that the dominant compression mechanisms for high volume filling factors are sliding and twisting motions, while rolling motion dominates for low volume filling factors. We confirm that our results are in good agreement with previous numerical studies. We suggest that our analytical formula is consistent with the previous experimental results if we assume the surface energy of silicate is ≃210 ± 90 mJ m−2. Now, we can apply our results to properties of small compact bodies, such as comets, asteroids, and pebbles. [ABSTRACT FROM AUTHOR]

A moving mass makes a gravitational wake in the partially ionized interstellar medium, which acts as a lens for radio-frequency light. Consequently, plasma microlensing could complement gravitational microlensing in the search for invisible massive objects, such as stellar remnants or compact dark matter. This work explores the spatial structure of the plasma lens associated with a gravitational wake. Far away from the moving mass, the characteristic lensing signal is the steady demagnification or magnification of a radio source as the wake passes in front of it at the speed of sound. Sources can be plasma-lensed at a much greater angular distance than they could be gravitationally lensed to the same degree by the same object. However, only the wakes of objects greatly exceeding stellar mass are expected to dominate over the random turbulence in the interstellar medium.

Collisionless systems often exhibit nonthermal power-law tails in their distribution functions. Interestingly, collisionless plasmas in various physical scenarios (e.g., the ion population of the solar wind) feature a v ^−5 tail in their velocity ( v ) distribution, whose origin has been a long-standing puzzle. We show this power-law tail to be a natural outcome of the collisionless relaxation of driven electrostatic plasmas. Using a quasi-linear analysis of the perturbed Vlasov–Poisson equations, we show that the coarse-grained mean distribution function (DF), f _0 , follows a quasi-linear diffusion equation with a diffusion coefficient D ( v ) that depends on v through the plasma dielectric constant. If the plasma is isotropically forced on scales larger than the Debye length with a white-noise-like electric field, D ( v ) ∼ v ^4 for σ < v < ω _P / k , with σ the thermal velocity, ω _P the plasma frequency, and k the characteristic wavenumber of the perturbation; the corresponding quasi-steady-state f _0 develops a v ^−( ^d ^ + 2) tail in d dimensions ( v ^−5 tail in 3D), while the energy ( E ) distribution develops an E ^−2 tail independent of dimensionality. Any redness of the noise only alters the scaling in the high v end. Nonresonant particles moving slower than the phase velocity of the plasma waves ( ω _P / k ) experience a Debye-screened electric field, and significantly less (power-law suppressed) acceleration than the near-resonant particles. Thus, a Maxwellian DF develops a power-law tail, while its core ( v < σ ) eventually also heats up but over a much longer timescale. We definitively show that self-consistency (ignored in test-particle treatments) is crucial for the emergence of the universal v ^−5 tail.

The centers of galaxies host a supermassive black hole (SMBH) surrounded by a dense stellar cluster. The cluster is expected to develop mass segregation, in which gravitational scatterings among the stars cause heavier objects to sink closer to the central black hole, while lighter objects will tend to be overconcentrated in the outer regions. This work focuses on the implications of mass segregation on the different channels for violent destruction of stars in the cluster: tidal disruptions, gravitational-wave-driven inspirals and high-velocity destructive collisions between stars. All such events occur close to the central black hole, where the heavier objects congregate. The analysis is based on a simplified Monte Carlo simulation, which evolves a two-mass population in a cluster surrounding a Milky Way–like SMBH. The simulation is based on the single-mass scheme used by Sari & Fragione and Balberg & Yassur, which has been extended to allow for the dynamical friction effects typical of unequal-mass populations. The effects of mass segregation on the rates of the different destruction channels are analyzed self-consistently in the overall evolution of the cluster. Also considered are stars which are injected into the cluster after being disrupted from a binary system by the SMBH. Such stars are captured in the inner regions of the cluster, and so their orbital evolution, as well as their destruction rate, are therefore influenced by heavy objects that might be abundant in the vicinity of the SMBH.

Structures in circumstellar matter reflect both fast processes and quasi-equilibrium states. A geometrical diversity of emitting circumstellar matter is observed around evolved massive stars, in particular around B[e] supergiants. We recapitulate classical analytical tools of linear and nonlinear potential theory, such as Cole–Hopf transformation and Grad–Shafranov theory, and develop them further to explain the occurrence of the circumstellar matter structures and their dynamics. We use potential theory to formulate the nonlinear hydrodynamical equations and test dilatations of the quasi-equilibrium initial conditions. We find that a wide range of flow patterns can basically be generated and the timescales can switch, based on initial conditions, and lead to eruptive processes, reinforcing that the nonlinear fluid environment includes both quasi-stationary structures and fast processes like finite-time singularities. Some constraints and imposed symmetries can lead to Keplerian orbits, while other constraints can deliver quasi-Keplerian ones. The threshold is given by a characteristic density at the stellar surface.

An event-based maximum likelihood method for handling X-ray polarimetry data is extended to include the effects of background and nonuniform sampling of the possible position angle space. While nonuniform sampling in position angle space generally introduces cross terms in the uncertainties of polarization parameters that could create degeneracies, there are interesting cases that engender no bias or parameter covariance. When including background in Poisson-based likelihood formulation, the formula for the minimum detectable polarization has nearly the same form as for the case of Gaussian statistics derived by Elsner et al. in the limiting case of an unpolarized signal. A polarized background is also considered, which demonstrably increases uncertainties in source polarization measurements. In addition, a Kolmogorov-style test of the event position angle distribution is proposed that can provide an unbinned test of models where the polarization angle in Stokes space depends on event characteristics such as time or energy.

Fine-tuning studies whether some physical parameters, or relevant ratios between them, are located within so-called life-permitting intervals of small probability outside of which carbon-based life would not be possible. Recent developments have found estimates of these probabilities that circumvent previous concerns of measurability and selection bias. However, the question remains whether fine-tuning can indeed be known. Using a mathematization of the concepts of learning and knowledge acquisition, we argue that most examples that have been touted as fine-tuned cannot be formally assessed as such. Nevertheless, fine-tuning can be known when the physical parameter is seen as a random variable and it is supported in the nonnegative real line, provided the size of the life-permitting interval is small in relation to the observed value of the parameter.

This work describes the illumination of exoplanets whose orbits are close enough to their host star that the finite angular size of their host star causes hyper illumination, in which more than 50% of the planet receives light. Such exoplanets include the hot Jupiters KELT-9 b (64.5% illuminated) and Kepler-91 b (69.6% illuminated). We describe the geometry of three primary illumination zones: the fully illuminated zone, penumbral zone, and unilluminated zone. The integrals required to determine the incident radiation as a function of position from the substellar point on the exoplanet are explained and derived, and the analytical solution is presented within the fully illuminated zone. We find that the illumination predicted by our model is greater at the substellar point than the typical plane-parallel ray model used would suggest. In addition, it is greater within the region of the penumbral zone extending into the antistellar side of the exoplanet. Finally, we compare our model to that used in starry, an open-source software package used to create albedo maps. It appears that starry may be overestimating the illumination of closely orbiting exoplanets because the foreshortening of the area element of the host star is not included in its calculation.

We present a general procedure for deriving a line-profile model for massive-star X-ray spectra that captures the dynamics of the wind more directly. The basis of the model is the analytic solution to the problem of variable jets in Herbig–Haro objects given by Cantó et al. In deriving our model, we generalize this jet solution to include flows with a prescribed nonzero acceleration for the context of radiatively driven winds. We provide example line profiles generated from our model for the case of sinusoidal velocity and mass-ejection variations. The example profiles show the expected shape of massive-star X-ray emission lines, as well as interesting but complicated trends with the model parameters. This establishes the possibility that observed X-rays could be a result of temporal variations seeded at the wind base, rather than purely generated intrinsically within the wind volume, and can be described via a quantitative language that connects with the physical attributes of those variations, consistently with the downstream momentum-conserving nature of radiatively cooled shocked radial flows.

JWST observations demonstrate that supermassive black holes (SMBHs) exist by redshifts z ≳ 10, providing further evidence for “direct collapse” black hole (BH) formation, whereby massive (∼10 ^3–5 M _⊙ ) SMBH seeds are generated within a few million years as a byproduct of the rapid inflow of gas into the centers of protogalaxies. Here we analyze the intermediate “quasi-star” phase that accompanies some direct-collapse models, during which a natal BH accretes mass from and energetically sustains (through accretion) an overlying gaseous envelope. We argue that previous estimates of the maximum BH mass that can be reached during this stage, ∼1% of the total quasi-star mass, are unphysical, and arise from underestimating the efficiency with which energy can be transported outward from regions close to the BH. We construct new quasi-star models that consist of an inner, “saturated convection” region (which conforms to a convection-dominated accretion flow near the BH) matched to an outer, adiabatic envelope. These solutions exist up to a BH mass of ∼60% of the total quasi-star mass, at which point the adiabatic envelope contains only 2% of the mass (with the remaining ∼38% in the saturated-convection region), and this upper limit is reached within a time of 20–40 Myr. We conclude that quasi-stars remain a viable route for producing SMBHs at large redshifts, which is consistent with recent JWST observations.

Placed slightly out of dynamical equilibrium, an isolated stellar system quickly returns toward a steady virialized state. We study this process of collisionless relaxation using the matrix method of linear response theory. We show that the full phase-space distribution of the final virialized state can be recovered directly from the disequilibrium initial conditions, without the need to compute the time evolution of the system. This shortcut allows us to determine the final virialized configuration with minimal computational effort. Complementing this result, we develop tools to model the system's full time evolution in the linear approximation. In particular, we show that moments of the velocity distribution can be efficiently computed using a generalized moment matrix. We apply our linear methods to study the relaxation of energy-truncated Hernquist spheres, mimicking the tidal stripping of a cuspy dark matter subhalo. Comparison of our linear predictions against controlled, isolated N -body simulations shows agreement at percent level for the parts of the system where a linear response to the perturbation is expected. We find that relaxation generates a tangential velocity anisotropy in the intermediate regions, despite the initial disequilibrium state having isotropic kinematics. Our results also strengthen the case for relaxation depleting the amplitude of the density cusp, without affecting its asymptotic slope. Finally, we compare the linear theory against an N -body simulation of tidal stripping on a radial orbit, confirming that the theory still accurately predicts density and velocity dispersion profiles for most of the system.

Magnetic helicity, H , measures magnetic linkages in a volume. The early theoretical development of helicity focused on magnetically closed systems in ${ \mathcal V }$ bounded by $\partial { \mathcal V }$ . For magnetically closed systems, ${ \mathcal V }\in {{\mathbb{R}}}^{3}={ \mathcal V }+{{ \mathcal V }}^{* }$ , no magnetic flux threads the boundary, $\hat{{\boldsymbol{n}}}\cdot {\boldsymbol{B}}{| }_{\partial { \mathcal V }}=0$ . Berger & Field and Finn & Antonsen extended the definition of helicity to relative helicity, ${ \mathcal H }$ , for magnetically open systems where magnetic flux may thread the boundary. Berger expressed this relative helicity as two gauge-invariant terms that describe the self-helicity of the magnetic field that closes inside ${ \mathcal V }$ and the mutual helicity between the magnetic field that threads the boundary $\partial { \mathcal V }$ and the magnetic field that closes inside ${ \mathcal V }$ . The total magnetic field that permeates ${ \mathcal V }$ entangles magnetic fields that are produced by current sources ${\boldsymbol{J}}$ in ${ \mathcal V }$ with magnetic fields that are produced by current sources ${\boldsymbol{J}}* $ in ${{ \mathcal V }}^{* }$ . Building on this fact, we extend Berger's expressions for relative magnetic helicity to eight gauge-invariant quantities that simultaneously characterize both of these self and mutual helicities and attribute their origins to currents ${\boldsymbol{J}}$ in ${ \mathcal V }$ and/or ${\boldsymbol{J}}* $ in ${{ \mathcal V }}^{* }$ , thereby disentangling the domain of origin for these entangled linkages. We arrange these eight terms into novel expressions for internal and external helicity (self) and internal-external helicity (mutual) based on their domain of origin. The implications of these linkages for interpreting magnetic energy are discussed and new boundary observables are proposed for tracking the evolution of the field that threads the boundary.

We propose a novel method to constrain the tidal quality factor, $Q^{\prime} $ , from an observed nonsynchronized star–planet system consisting of a slowly rotating low-mass star and a close-in Jovian planet, taking into account the coevolution of stellar spin and planetary orbit due to the tidal interaction and the magnetic braking. On the basis of dynamical system theory, the track of the coevolution of angular momentum from the fast-rotator regime for such a system exhibits the existence of a forbidden region in the Ω _orb –Ω _spin plane, where Ω _spin and Ω _orb denote the angular velocity of the stellar spin and planetary orbit, respectively. The forbidden region is determined primarily by the strength of the tidal interaction. By comparing the (Ω _orb , Ω _spin ) of a single star–planet system to the forbidden region, we can constrain the tidal quality factor regardless of the evolutionary history of the system. The application of this method to the star–planet system NGTS-10–NGTS-10 b gives $Q^{\prime} \gtrsim {10}^{8}$ , leading to a tight upper bound on the tidal torque. Since this cannot be explained by previous theoretical predictions for nonsynchronized star–planet systems, our result requires mechanisms that suppress the tidal interaction in such systems.

High-spatial-resolution images of the solar corona acquired in the extreme ultraviolet (EUV), most notably with the Atmospheric Imaging Assembly (AIA) instrument on the Solar Dynamics Observatory (SDO) reveal the abundance of dynamic events which range from flaring bright points and jets to erupting prominences and coronal mass ejections (CMEs). In this work we present novel techniques to extract such dynamic events from the more steady background corona using 17.1 nm SDO-AIA images. The techniques presented here treat any time series of coronal images as a matrix that can be decomposed into two matrices representing the background and the dynamic component, respectively. The latter has the properties of a so-called sparse matrix, and the proposed methods are classified as methods based on sparse representations. The proposed methods are the median-filter method, the principal component pursuit, and the dynamic-mode decomposition, all of which include data pre-processing using the noise-adaptive fuzzy equalization method. The study reveals that the median-filter method and the dynamic-mode decomposition enhance all motions in the time series and produce similar results. On the other hand, the principal component pursuit enables the clear differentiation of CMEs from the background corona, thus providing a valuable tool for the characterization of their acceleration profiles in the low corona as seen in the EUV.

[Display omitted] • Intrinsic nature of catalysis is revealed with Polanyi and Bronsted relations. • Optimality in catalysis is a subtle balance of coordinated kinetic-related factors. • Analytical mathematics approach manifests essential key equations for kinetic studies Inherent nature of a heterogeneous catalytic reaction system represented by a correlation between kinetics and thermodynamics is revealed as harmonious coordination of the correlation parameter and the binding state of a key adsorbate when the system is at the optimum condition with maximum reaction rate. This interpretation comes from the newly obtained common results in different reaction settings and conveys the essence of the catalytic reaction. Pioneering work by Michel Boudart in 1968 based on Polanyi and Bronsted relations was a key guidance to an extended development by the present author in 1988. And now further advancement has been made and it leads us to conclude that if the reaction system follows such a correlation, there is a systematic framework acting to orchestrate the best reaction performance. This framework is an intrinsic part of catalysis. In consequence, a new definition is suggested for the extended Sabatier's principle. The efficacy and profundity of analytical mathematics approach appear in the key equations as they disclose the fundamental nature of catalytic reactions. The optimum in catalysis is a delicately controlled state made possible by an essential balance between kinetics and thermodynamics. [ABSTRACT FROM AUTHOR]

The simplest restricted three-body problem, in which two massive points and a massless point particle attract one another according to Newton’s law of inverse squares, has pulsating Hill’s regions where the massless particle moves inside the closed regions surrounding only one of the massive points. Until now, no numerical integrator is known to maintain these regions, making it challenging to reproduce the phenomenon of gravitational capture of massless particles. In this article, we propose a second-order integrator that preserves Hill’s regions to accurately simulate this phenomenon. Our integrator is based on a logarithmic Hamiltonian leapfrog method developed by Mikkola and Tanikawa and features a parameter that is adjusted to preserve a second-order approximation of an invariant integration relation of this restricted three-body problem. We analytically and numerically clarify that this integrator has the following properties: (i) it retains the collinear and triangular Lagrangian solutions regardless of the eccentricity of the relative orbit of the two massive points, (ii) it has the same Hill stability criterion for satellite-type motion of the massless point particle as the original problem, and (iii) it conserves the Jacobi integral for zero eccentricity.

The centers of galaxies host both a supermassive black hole and a dense stellar cluster. Such an environment should lead to stellar collisions, possibly at very high velocities so that the total energy involved is of the same order as supernova explosions. We present a simplified numerical analysis of the destructive stellar collision rate in a cluster similar to that of the Milky Way. The analysis includes an effective average two-body relaxation Monte Carlo scheme and general relativistic effects, as used by Sari & Fargione, to which we added explicit tracking of local probabilities for stellar collisions. We also consider stars which are injected into the stellar cluster after being disrupted from a binary system by the supermassive black hole. Such stars are captured in the vicinity of the black hole and enhance the expected collision rate. In our results we examine the rate and energetic distribution function of high-velocity stellar collisions, and compare them self-consistently with the other destructive processes which occur in the galactic center, namely tidal disruptions and extreme mass ratio inspirals.

Most studies of the 3D density structure of prestellar cores have used isotropic evolution models, which are projected into 2D for direct comparison with observation data. In this study, we introduced the anisotropic inverse Abel transform method for reconstructing the 3D volume density profile of prestellar cores. We demonstrated that this approach could accurately preserve information about the realistic 3D structure with numerical simulation. This method has great advantages compared to the shape-assumption methods, particularly in high-density regions. We applied this method to the Herschel 2D column density maps of three prestellar cores, and the results showed good agreement with theoretical models. By changing the direction of the inversion axis of symmetry, we confirmed that the density profiles of prestellar cores exhibit nearly cylindrical symmetry.

Some massive stars likely fail to produce core-collapse supernovae, but these failed supernovae (FSNe) can generate an electromagnetic outburst prior to the disappearance of the star, as the mass lost to neutrinos during the stellar core collapse results in the formation and breakout of a second shock. We show that, when the mass lost to neutrinos is sufficiently small, there are two self-similar solutions that describe the propagation of a weak shock into a hydrodynamically expanding envelope that simultaneously yield accretion onto the black hole. The larger Mach number solution is unstable and yields the minimum Mach number that a shock must have to strengthen into the energy-conserving regime. Above a critical mass loss, there are no weak-shock solutions, implying that there are only strong explosions if the neutrino mass loss is above a critical value, and this value is a few percent of the mass of the star (and is physically achievable) for typical parameters. Our results imply that the fate of the explosion from an FSN—weak with little to no mass ejection or strong with the expulsion of the majority of the envelope—is a sensitive function of the stellar properties and the neutrino mass loss. We also show that there is a second type of self-similar solution for the shock that results in the settling of the gas near the compact object, which may be applicable to nonterminal stellar eruptions and the response of a gaseous disk to gravitational-wave induced mass loss from a binary black hole merger.

The presence of tidal deformations in close binary stars has already been confirmed by astronomical observations. The present paper aims to simply address an astronomy problem, studying the relative movement of close binaries disturbed by their mutual deformation through some basic concepts and tools of celestial mechanics. For this purpose, the tidal effect is modeled by considering that each star is an elongated revolution ellipsoid in such a way that axes of revolution are coincident, and their largest axes point toward each other along the motion. The potential for mutual attraction is then obtained, resulting in a perturbed Keplerian system with perturbation proportional to the inverse of the cubic distance between the stars, thus being a one-degree-of-freedom problem and, therefore, integrable. The effective potential, the integrals of energy and angular momentum, and the Laplace vector are used to obtain qualitative information about the dynamics before integrating it. The motion describes a rosette-like orbit with periodic osculating elements, or a circle when the energy is a local minimum. Finally, an analytical solution is presented in terms of elliptic functions by using a regularizing and linearizing function.

The use of Gaussian processes (GPs) as models for astronomical time series data sets has recently become almost ubiquitous, given their ease of use and flexibility. In particular, GPs excel at marginalization over the stellar signal when the variability due to starspots is treated as a nuisance, as in exoplanet transit modeling. However, these effective models are less useful in cases where the starspot signal is of primary interest, since it is not obvious how the parameters of the GP relate to physical parameters like the spot size, contrast, and latitudinal distribution. Instead, it is common practice to explicitly model the effect of individual starspots on the light curve and attempt to infer their properties via optimization or posterior inference. Unfortunately, this process is ill-posed and often computationally intractable when applied to stars with more than a few spots and/or to ensembles of many stars. Here we derive a closed-form expression for a GP that describes the light curve of a rotating, evolving stellar surface conditioned on a given distribution of starspot sizes, contrasts, and latitudes. We demonstrate that this model is correctly calibrated, allowing one to robustly infer physical parameters of interest from one or more light curves, including the typical spot radii and latitudes. Our GP has far-ranging implications for understanding the variability and magnetic activity of stars from light curves and radial velocity measurements, as well as for modeling correlated noise in exoplanet searches. Our implementation is efficient, user-friendly, and open-source, available in the package starry _ process . https://github.com/rodluger/starry_process

This review essay introduces the work of the Egyptian scientific historian and philosopher Roshdi Rashed, a pioneer in the field of the history of Arab sciences. The article is based on the five volumes he originally wrote in French and later translated into Arabic, which were published by the Centre for Arab Unity Studies and which are now widely acclaimed as a unique effort to unveil the achievements of Arab scientists. The essay reviews this major work, which seems, like Plato's Republic to have "No Entry for Those Who Have No Knowledge of Mathematics" written on its gate. If you force your way in, even with elementary knowledge of computation, a philosophy will unfold before your eyes, described by the Italian astronomer Galileo Galilei as "written in that great book which ever lies before our eyes--I mean the universe--but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth." The essay is a journey through this labyrinth where the history of world mathematics got lost and was chronicled by Rashed in five volumes translated from the French into Arabic. It took him fifteen years to complete. [ABSTRACT FROM AUTHOR]