Keywords

In this work the influence of the post-Newtonian corrections to the equations of stellar structure are analyzed. The post-Newtonian Lane–Emden equation follows from the corresponding momentum density balance equation. From a polytropic equation of state the solutions of the Lane–Emden equations in the Newtonian and post-Newtonian theories are determined and the physical quantities for the Sun, the white dwarf Sirius B and neutron stars with masses M ≃ 1.4 M_⊙, 1.8 M_⊙ and 2.0 M_⊙ are calculated. It is shown that the post-Newtonian corrections to the fields of mass density, pressure and temperature are negligible for the Sun and Sirius B, but for stars with strong fields the differences become important. For the neutron stars analyzed here the central pressure and the central temperature which follow from the post-Newtonian Lane–Emden equation are about fifty to sixty percent greater than those of the Newtonian theory and the central mass density is about three to four percent smaller.

Applying functional differentiation to the density field with Newtonian gravity, we obtain the static, nonlinear equation of the three-point correlation function ζ of galaxies to the third order density perturbations. We make the equation closed and perform renormalization of the mass and the Jeans wavenumber. Using the boundary condition inferred from observations, we obtain the third order solution ζ(r, u, θ) at fixed u = 2, which is positive, exhibits a U-shape along the angle θ, and decreases monotonously along the radial r up to the range r ≤ 30 h⁻¹ Mpc in our computation. The corresponding reduced Q(r, u, θ) deviates from 1 of the Gaussian case, has a deeper U-shape along θ, and varies non-monotonously along r. The third order solution agrees with the SDSS data of galaxies, quite close to the previous second order solution, especially at large scales. This indicates that the equations of correlation functions with increasing orders of density perturbation provide a stable description of the nonlinear galaxy system.

We present a carefully designed, systematic study of the angular resolution dependence of simulations with the Prometheus-Vertex neutrino-hydrodynamics code. Employing a simplified neutrino heating–cooling scheme in the Prometheus hydrodynamics module allows us to sample the angular resolution between 4° and 05. With a newly implemented static mesh refinement (SMR) technique on the Yin-Yang grid, the angular coordinates can be refined in concentric shells, compensating for the diverging structure of the spherical grid. In contrast to previous studies with Prometheus and other codes, we find that higher angular resolution and therefore lower numerical viscosity provides more favorable explosion conditions and faster shock expansion. We discuss the possible reasons for the discrepant results. The overall dynamics seem to converge at a resolution of about 1°. Applying the SMR setup to marginally exploding progenitors is disadvantageous for the shock expansion, however, because the kinetic energy of downflows is dissipated to internal energy at resolution interfaces, leading to a loss of turbulent pressure support and a steeper temperature gradient. We also present a way to estimate the numerical viscosity on grounds of the measured turbulent kinetic energy spectrum, leading to smaller values that are better compatible with the flow behavior witnessed in our simulations than results following calculations in previous literature. Interestingly, the numerical Reynolds numbers in the turbulent, neutrino-heated postshock layer (some 10 to several hundred) are in the ballpark of expected neutrino drag effects on the relevant length scales. We provide a formal derivation and quantitative assessment of the neutrino drag terms in an appendix.

The emission from dark ages halos in the lines of transitions between the lowest rotational levels of hydrogen and hydrogen deuteride molecules is analyzed. It is assumed that molecules are excited by the cosmic microwave background (CMB) and collisions with hydrogen atoms. The physical parameters of halos and the number density of molecules are precalculated assuming that halos are homogeneous top-hat spheres formed from the cosmological density perturbations in the four-component universe with post-Planck cosmological parameters. The differential brightness temperatures and differential spectral fluxes in the rotational lines of H₂–HD molecules are computed for two phenomena: thermal luminescence and resonant scattering of CMB radiation. The results show that the expected maximal values of differential brightness temperature of warm halos (T_K ∼ 200–800 K) are at the level of nanokelvins, are comparable for both phenomena, and are below the sensitivity of modern submillimeter radio telescopes. For hot halos (T_K ∼ 2000–5000 K) the thermal emission of H₂-ortho molecules dominates and the differential brightness temperatures are predicted to be of a few microkelvins at the frequencies 300–600 GHz, which could be detectable with next-generation telescopes.

Most one-dimensional core-collapse simulations fail to explode, yet multidimensional simulations often explode. A dominant multidimensional effect aiding explosion is neutrino-driven convection. We incorporate a convection model in approximate one-dimensional core-collapse supernova (CCSN) simulations. This is the 1D+ method. This convection model lowers the neutrino luminosity required for explosion by $\sim 30$%, similar to the reduction observed in multidimensional simulations. The model is based upon the global turbulence model of Mabanta & Murphy and models the mean-field turbulent flow of neutrino-driven convection. In this preliminary investigation, we use simple neutrino heating and cooling algorithms to compare the critical condition in the 1D+ simulations with the critical condition observed in two-dimensional simulations. Qualitatively, the critical conditions in the 1D+ and the two-dimensional simulations are similar. The assumptions in the convection model affect the radial profiles of density, entropy, and temperature, and comparisons with the profiles of three-dimensional simulations will help to calibrate these assumptions. These 1D+ simulations are consistent with the profiles and explosion conditions of equivalent two-dimensional CCSN simulations but are ∼10² times faster, and the 1D+ prescription has the potential to be ∼10⁵ faster than three-dimensional CCSN simulations. With further calibration, the 1D+ technique could be ideally suited to test the explodability of thousands of progenitor models.

We investigate the interaction between active galactic nucleus (AGN) jets and the intracluster medium (ICM) of galaxy clusters. Specifically, we study the efficiency with which jets can drive sound waves into the ICM. Previous works focused on this issue model the jet–ICM interaction as a spherically symmetric explosion, finding that ≲12.5% of the blast energy is converted into sound waves, even for instantaneous energy injection. We develop a method for measuring sound wave energy in hydrodynamic simulations and measure the efficiency of sound wave driving by supersonic jets in a model ICM. Our axisymmetric fiducial simulations convert ≳25% of the jet energy into strong, long-wavelength sound waves that can propagate to large distances. Vigorous instabilities driven by the jet–ICM interaction generate small-scale sound waves that constructively interfere, forming powerful large-scale waves. By scanning a parameter space of opening angles, velocities, and densities, we study how our results depend on jet properties. High-velocity, wide-angle jets produce sound waves most efficiently, yet the acoustic efficiency never exceeds 1/3 of the jet energy—an indication that equipartition may limit the nonlinear energy conversion process. Our work argues that sound waves may compose a significant fraction of the energy budget in cluster AGN feedback and underscores the importance of properly treating compressive wave dissipation in the weakly collisional, magnetized ICM.

We have studied double-detonation explosions in double-degenerate (DD) systems with different companion white dwarfs (WDs) for modeling Type Ia supernovae (SNe Ia) by means of high-resolution smoothed particle hydrodynamics (SPH) simulations. We have found that only the primary WDs explode in some of the DD systems, while the explosions of the primary WDs induce the explosions of the companion WDs in the other DD systems. The former case is a so-called dynamically-driven double-degenerate double-detonation (D⁶) explosion, or helium-ignited violent merger explosion. The SN ejecta of the primary WDs strip materials from the companion WDs, whose mass is ∼10⁻³ M_⊙. The stripped materials contain carbon and oxygen when the companion WDs are carbon–oxygen (CO) WDs with He shells ≲0.04 M_⊙. Since they contribute to low-velocity ejecta components as observationally inferred for iPTF14atg, D⁶ explosions can be counterparts of subluminous SNe Ia. The stripped materials may contribute to low-velocity C seen in several SNe Ia. In the latter case, the companion WDs explode through He detonation if they are He WDs and through the double-detonation mechanism if they are CO WDs with He shells. We name these explosions "triple" and "quadruple" detonation (TD/QD) explosions after the number of detonations. The QD explosion may be counterparts of luminous SNe Ia, such as SN 1991T and SN 1999aa, since they yield a large amount of ⁵⁶Ni, and their He-detonation products contribute to the early emissions accompanying such luminous SNe Ia. On the other hand, the TD explosion may not yield a sufficient amount of ⁵⁶Ni to explain luminous SNe Ia.

The streaming instability (SI) is a mechanism to aerodynamically concentrate solids in protoplanetary disks and facilitate the formation of planetesimals. Recent numerical modeling efforts have demonstrated the increasing complexity of the initial mass distribution of planetesimals. To better constrain this distribution, we conduct SI simulations including self-gravity with the highest resolution hitherto. To subsequently identify all of the self-bound clumps, we develop a new clump-finding tool, Planetesimal Analyzer. We then apply a maximum likelihood estimator to fit a suite of parameterized models with different levels of complexity to the simulated mass distribution. To determine which models are best-fitting and statistically robust, we apply three model selection criteria with different complexity penalties. We find that the initial mass distribution of clumps is not universal regarding both the functional forms and parameter values. Our model selection criteria prefer models different from those previously considered in the literature. Fits to multi-segment power-law models break to a steeper distribution above masses close to those of 100 km collapsed planetesimals, similar to observed size distributions in the Kuiper Belt. We find evidence for a turnover at the low-mass end of the planetesimal mass distribution in our high-resolution run. Such a turnover is expected for gravitational collapse, but had not previously been reported.

We examine the possible role of turbulence in feeding the emission of gamma-ray bursts (GRBs). Turbulence may develop in a GRB jet as the result of hydrodynamic or current-driven instabilities. The jet carries dense radiation and the turbulence cascade can be damped by Compton drag, passing kinetic fluid energy to photons through scattering. We identify two regimes of turbulence dissipation: (1) "Viscous"—the turbulence cascade is Compton-damped on a scale ${{\ell }}_{\mathrm{damp}}$ greater than the photon mean free path ${{\ell }}_{\star }$. Then turbulence energy is passed to photons via bulk Comptonization by smooth shear flows on scale ${{\ell }}_{\star }\lt {{\ell }}_{\mathrm{damp}}$. (2) "Collisionless"—the cascade avoids Compton damping and extends to microscopic plasma scales much smaller than ${{\ell }}_{\star }$. The collisionless dissipation energizes plasma particles, which radiate the received energy; how the dissipated power is partitioned between particles needs further investigation with kinetic simulations. We show that the dissipation regime switches from viscous to collisionless during the jet expansion, at a critical value of the jet optical depth, which depends on the amplitude of turbulence. Turbulent GRB jets are expected to emit nonthermal photospheric radiation. Our analysis also suggests revisions of turbulent Comptonization in black hole accretion disks discussed in previous works.

Thermal nonequilibrium (TNE) is a fascinating situation that occurs in coronal magnetic flux tubes (loops) for which no solution to the steady-state fluid equations exists. The plasma is constantly evolving even though the heating that produces the hot temperatures does not. This is a promising explanation for isolated phenomena such as prominences, coronal rain, and long-period pulsating loops, but it may also have much broader relevance. As known for some time, TNE requires that the heating be both (quasi-)steady and concentrated at low coronal altitudes. Recent studies indicate that asymmetries are also important, with large enough asymmetries in the heating and/or cross-sectional area resulting in steady flow rather than TNE. Using reasonable approximations, we have derived two formulae for quantifying the conditions necessary for TNE. As a rough rule of thumb, the ratio of apex to footpoint heating rates must be less than about 0.1, and asymmetries must be less than about a factor of 3. The precise values are case-dependent. We have tested our formulae with 1D hydrodynamic loop simulations and find a very acceptable agreement. These results are important for developing physical insight about TNE and assessing how widespread it may be on the Sun.