Standing Shock Wave Research Articles

Detectability of Late-time Supernova Neutrinos with Fallback Accretion onto Protoneutron Star

We investigate the late-time neutrino emission powered by fallback mass accretion onto a protoneutron star (PNS), using neutrino radiation-hydrodynamic simulations with full Boltzmann neutrino transport. We follow the time evolution of the accretion flow onto the PNS until the system reaches a quasi-steady state. A standing shock wave is commonly formed in the accretion flow, whereas the shock radius varies depending on the mass accretion rate and the PNS mass. A sharp increase in temperature emerges in the vicinity of the PNS (∼10 km), which characterizes neutrino emission. Both the neutrino luminosity and the average energy become higher with increasing mass accretion rate and PNS mass. The mean energy of the emitted neutrinos is in the range of 10 ≲ ϵ ≲ 20 MeV, which is higher than that estimated from PNS cooling models (≲10 MeV). Assuming a distance to core-collapse supernova of 10 kpc, we quantify neutrino event rates for Super-Kamiokande (Super-K) and Deep Underground Neutrino Experiment (DUNE). The estimated detection rates are well above the background, and their energy-dependent features are qualitatively different from those expected from PNS cooling models. Another notable feature is that the neutrino emission is strongly flavor dependent, exhibiting that the neutrino event rate hinges on the neutrino oscillation model. We estimate them in the case with the adiabatic Mikheev–Smirnov–Wolfenstein model, and show that the normal and inverted mass hierarchy offer a large number of neutrino detections in Super-K and DUNE, respectively. Hence the simultaneous observation with Super-K and DUNE of fallback neutrinos will provide a strong constraint on the neutrino mass hierarchy.

A domain decomposition technique for acoustic wave interactions and scattering

In this work, a two-dimensional domain decomposition technique (DDT) is developed based on an overset method that couples a nonlinear Euler solver with a linearized Euler solver. The nonlinear domain accounts for complex physics in the near field, such as acoustic wave interaction with shock waves and acoustic wave scattering from solid bodies. The linear domain allows the small perturbation waves induced by the nonlinear effects to propagate with minimal numerical dissipation and dispersion while also significantly reducing computational resources. To this end, two scenarios have been considered: (i) wave amplification and modulation in a converging-diverging duct with a standing shock wave and (ii) wave scattering from an incident acoustic wave over a supercritical airfoil. With DDT, these cases show a reduction in computational time by more than 70% compared to their respective fully-nonlinear simulations. The accuracy of the simulations with DDT is found to depend on the extent of overlap between the linear and nonlinear zones. In general, an overlap ratio of at least two is necessary to maintain high order of convergence rate, though still limited by the nonlinear scheme. Furthermore, the implementation of DDT in the external flow case can eliminate numerical noise observed at the far field of the fully-nonlinear counterpart, which do not have any effective non-reflecting boundary treatment.

Disc accretion shocks with alpha viscosity

ABSTRACT Shocks in rotating disc accretion flows under the vertically hydrostatic equilibrium are examined, taking into account the α viscosity. For the case that the stress tensor is proportional to the gas pressure, and neglects the effects of the mixture of gas and radiation pressure, we derive analytical expressions for jump conditions of disc accretion shocks with alpha viscosity; they would be useful for various disc accretion problems. As in the usual accretion disc, the alpha viscosity works as angular momentum transport and heat generation. When a steadily standing shock wave is generated in a disc, due to the viscous effect, the azimuthal velocity discontinuously decreases in the post-shock region inside the front. For sufficiently strong shocks, the post-shock azimuthal velocity vanishes; in other words, the rotating accretion flows turn to the radially accretion ones, after passing the shock front. This vanishing condition is roughly expressed as $\alpha {\cal M}_1/{\cal M}_{\varphi 1}$ 1, where α is the viscous alpha parameter, ${\cal M}_1$ the pre-shock radial Mach number, and ${\cal M}_{\varphi 1}$ the pre-shock azimuthal Mach number. Furthermore, due to the viscous heating, the disc height increases and the surface density decreases in the post-shock region, compared to the non-viscous case. This angular momentum transport via disc shocks would affect the accretion spin-up of the central objects and accretion problems in general.

Development of Choked Flow in Variable Nozzle Radial Turbines

In commonly applied one-dimensional choking models for radial turbines, choked flow is assumed to appear in the geometrical throat of each stator and rotor. Coupled and complex three-dimensional effects are not considered. In order to analyze the internal aerodynamic in a radial turbine at off design conditions and before carrying out experimental tests, which in the case of automotive turbocharger are limited by their compact size, computational fluid dynamics (CFD) simulations stand out as a useful tool. This paper presents the study of a variable geometry turbine (VGT) of a commercial turbocharger at off design conditions reaching choked flow, analyzing the presence of this limiting conditions in the stator and rotor under different operation points and VGT positions. Reynolds-averaged Navier-Stokes (RANS) and unsteady RANS simulation have been performed to obtain the flow structures in stator and rotor. The results reveal that the choked effective area mostly depends on the stator vane position and pressure ratio. For the closed VGT position a standing shock wave appears on the stator suction side and expands through the vaneless space. For the opened VGT position the flow is choked at the rotor outlet. However, the evolution of the choked area highly depends on the rotational speed and the secondary flow. A strong interaction with the tip leakage vortex has been identified.

Flux variability from ejecta in structured relativistic jets with large-scale magnetic fields

Context. Standing and moving shocks in relativistic astrophysical jets are very promising sites for particle acceleration to large Lorentz factors and for the emission from the radio up to the γ-ray band. They are thought to be responsible for at least part of the observed variability in radio-loud active galactic nuclei. Aims. We aim to simulate the interactions of moving shock waves with standing recollimation shocks in structured and magnetized relativistic jets and to characterize the profiles of connected flares in the radio light curve. Methods. Using the relativistic magneto-hydrodynamic code MPI-AMRVAC and a radiative transfer code in post-processing, we explore the influence of the magnetic-field configuration and transverse stratification of an over-pressured jet on its morphology, on the moving shock dynamics, and on the emitted radio light curve. First, we investigate different large-scale magnetic fields with their effects on the standing shocks and on the stratified jet morphology. Secondly, we study the interaction of a moving shock wave with the standing shocks. We calculated the synthetic synchrotron maps and radio light curves and analyze the variability at two frequencies 1 and 15.3 GHz and for several observation angles. Finally, we compare the characteristics of our simulated light curves with radio flares observed from the blazar 3C 273 with the Owens Valley Radio Observatory and Very Long Baseline Array in the MOJAVE survey between 2008 and 2019. Results. We find that in a structured over-pressured relativistic jet, the presence of the large-scale magnetic field structure changes the properties of the standing shock waves and leads to an opening in the jet. The interaction between waves from inner and outer jet components can produce strong standing shocks. When crossing such standing shocks, moving shock waves accompanying overdensities injected in the base of the jet cause very luminous radio flares. The observation of the temporal structure of these flares under different viewing angles probes the jet at different optical depths. At 1 GHz and for small angles, the self-absorption caused by the moving shock wave becomes more important and leads to a drop in the observed flux after it interacts with the brightest standing knot. A weak asymmetry is seen in the shape of the simulated flares, resulting from the remnant emission of the shocked standing shocks. The characteristics of the simulated flares and the correlation of peaks in the light curve with the crossing of moving and standing shocks favor this scenario as an explanation of the observed radio flares of 3C 273.

Inlet air and fuel flow pressure fluctuation effect on supersonic combustion

PurposeThe purpose of this paper is to analyze the effect of pressure fluctuations on the combustion efficiency of the hydrogen fuel injected into the supersonic oxidizing cross flow. The pressure fluctuations are imposed on inlet air flow and also on the fuel flow stream. Two different situations are considered: the combustion chamber once without and again with the inlet standing oblique shock wave.Design/methodology/approachThe pressure fluctuations are imposed on inlet air flow and also on the fuel flow stream. Two different situations are considered: the combustion chamber once without and again with the inlet standing oblique shock wave. The unsteady turbulent reacting flow solver is developed to simulate the supersonic flow field in the combustion chamber with detail chemical kinetics, to predict the time-variation of the combustion efficiency due to the imposed pressure fluctuations.FindingsThe results show that the response of the reacting flow field depends on both the frequency of fluctuations and the existence of the inlet shock wave. In addition, the inlet standing shock wave has some attenuating role, but the reacting flow shows an amplifying role on imposed oscillations which is also augmented by imposing anti-phase fluctuations on both inlet and fuel flow streams.Originality/valueThis study is performed to analyze the instabilities in the supersonic combustion which has not been considered before in this manner.

Solar Radio Bursts Associated with Standing Shock Waves

A number of phenomena with radio bursts in the decimeter and centimeter wavelength ranges similar to type-II bursts in the meter range have been considered. In all phenomena, the radio bursts are characterized by the cessation of frequency drift and its reversal. Analysis of all of the available data on relevant bursts provides evidence of termination shocks with particle accelerations in their fronts. This is confirmed by the generation of new sources of hard X-ray radiation and the radio emission of fast bursts (spikes), fibers, and zebra structures. The sources of drift stripes with a drift turn are located either between the burst loop and the lower shock wave or between the lower and upper shock waves. Estimates of the critical Mach number for common parameters of the burst plasma indicated that the values (Mcr = 1.1–1.3) can easily be observed in the given phenomena and that the radiation can be associated with the Buneman instability. The conditions necessary for the generation of observed electromagnetic radiation bursts can be provided in helmet-shaped magnetic structures in the solar corona.

Sparks May Reveal the Nature of Ash Plumes

In lab experiments and models, researchers uncover how ash can affect the standing shock waves of erupting volcanoes. Their findings may lead to new predictions of volcanic ash hazards.

Effects of Rotation and Magnetic Field on the Revival of a Stalled Shock in Supernova Explosions

Abstract We investigate axisymmetric steady solutions of (magneto)hydrodynamics equations that approximately describe accretion flows through a standing shock wave onto a protoneutron star and discuss the effects of rotation and magnetic field on the revival of the stalled shock wave in supernova explosions. We develop a new powerful numerical method to calculate the two-dimensional steady accretion flows self-consistently. We first confirm the results of preceding papers that there is a critical luminosity of irradiating neutrinos, above which there exists no steady solution in spherical models. If a collapsing star is rotating and/or has a magnetic field, the accretion flows are no longer spherical owing to the centrifugal force and/or Lorentz force, and the critical luminosity is modified. In fact, we find that the critical luminosity is reduced by about 50%–70% for very rapid rotations; the rotation frequencies are 0.2–0.45 s−1 at the radius of r = 1000 km (equivalent to spin periods ∼0.5–0.22 ms at r = 10 km) and about 20%–50% for strong toroidal magnetic fields (the strengths of which are 1.0 × 1012–3.0 × 1012 G at r = 1000 km), depending on the mass accretion rate. These results may also be interpreted as the existence of a critical specific angular momentum or critical magnetic field, above which there exists no steady solution and the standing shock wave will be revived for a given combination of mass accretion rate and neutrino luminosity.

Standing shocks in magnetized advection accretion flows onto a rotating black hole

We present the global structure of magnetized advective accretion flow around the rotating black holes in presence of dissipation. By considering accretion flow to be threaded by toroidal magnetic fields and by assuming synchrotron radiative mechanism to be the dominant cooling process, we obtain global transonic accretion solutions in terms of dissipation parameters, such as viscosity ($\alpha_B$), accretion rate (${\dot m}$) and plasma-$\beta$, respectively. In the rotating magnetized accretion flow, centrifugal barrier is developed in the nearby region of the black hole that triggers the discontinuous shock transition in the flow variables. Evidently, the shock properties and the dynamics of the post-shock flow (hereafter post-shock corona (PSC)) are being governed by the flow parameters. We study the role of dissipation parameters in the formation of standing shock wave and find that global shocked accretion solutions exist both in gas pressure dominated flows and in magnetic pressure dominated flows. In addition, we observe that standing shock continues to form around the rapidly rotating black holes as well. We identify the range of dissipation parameters that permits shocked accretion solutions and find that standing shocks continue to form even in presence of high dissipation limit, although the likelihood of shock formation diminishes with the increase of dissipation. Further, we compute the critical accretion rate (${\dot m}^{\rm cri}$) that admits shock and observe that standing shock exists in a magnetically dominated accretion flow when the accretion rate lies in general in the sub-Eddington domain. At the end, we calculate the maximum dissipated energy that may be escaped from the PSC and indicate its possible implication in the astrophysical context.

Properties of two-temperature dissipative accretion flow around black holes

We study the properties of two-temperature accretion flow around a non-rotating black hole in presence of various dissipative processes where pseudo-Newtonian potential is adopted to mimic the effect of general relativity. The flow encounters energy loss by means of radiative processes acted on the electrons and at the same time, flow heats up as a consequence of viscous heating effective on ions. We assumed that the flow is exposed with the stochastic magnetic fields that leads to Synchrotron emission of electrons and these emissions are further strengthen by Compton scattering. We obtain the two-temperature global accretion solutions in terms of dissipation parameters, namely, viscosity (α) and accretion rate (⁠|${\dot{m}}$|⁠), and find for the first time in the literature that such solutions may contain standing shock waves. Solutions of this kind are multitransonic in nature, as they simultaneously pass through both inner critical point (xin) and outer critical point (xout) before crossing the black hole horizon. We calculate the properties of shock-induced global accretion solutions in terms of the flow parameters. We further show that two-temperature shocked accretion flow is not a discrete solution, instead such solution exists for wide range of flow parameters. We identify the effective domain of the parameter space for standing shock and observe that parameter space shrinks as the dissipation is increased. Since the post-shock region is hotter due to the effect of shock compression, it naturally emits hard X-rays, and therefore, the two-temperature shocked accretion solution has the potential to explain the spectral properties of the black hole sources.

Heliospheric modulation of cosmic rays: model and observation

This paper presents the basic model of cosmic ray modulation in the heliosphere, developed in Yu.G. Shafer Institute of Cosmophysical Research and Aeronomy of the Siberian Branch of RAS. The model has only one free modulation parameter: the ratio of the regular magnetic field to the turbulent one. It may also be applied to the description of cosmic ray intensity variations in a wide energy range from 100 MeV to 100 GeV. Possible mechanisms of generation of the mentioned turbulence field are considered. The primary assumption about the electrical neutrality of the heliosphere appears to be wrong, and the zero potential needed to match the model with observations in the plane of the solar equator can be achieved if the frontal point of the heliosphere, which is flowed around by interstellar gas, lies near the mentioned plane. We have revealed that the abnormal rise of cosmic ray intensity at the end of solar cycle 23 is related to the residual modulation produced by the subsonic solar wind behind the front of a standing shock wave. The model is used to describe features of cosmic ray intensity variations in several solar activity cycles.

Гелиосферная модуляция космических лучей: модель и наблюдения

This paper presents the basic model of cosmic ray modulation in the heliosphere, developed in Yu.G. Shafer Institute of Cosmophysical Research and Aeronomy of the Siberian Branch of RAS. The model has only one free modulation parameter: the ratio of the regular magnetic field to the turbulent one. It may also be applied to the description of cosmic ray intensity variations in a wide energy range from 100 MeV to 100 GeV. Possible mechanisms of generation of the mentioned turbulence field are considered. The primary assumption about the electrical neutrality of the heliosphere appears to be wrong, and the zero potential needed to match the model with observations in the plane of the solar equator can be achieved if the frontal point of the heliosphere, which is flowed around by interstellar gas, lies near the mentioned plane. We have revealed that the abnormal rise of cosmic ray intensity at the end of solar cycle 23 is related to the residual modulation produced by the subsonic solar wind behind the front of a standing shock wave. The model is used to describe features of cosmic ray intensity variations in several solar activity cycles.

A two-fluid model for black-hole accretion flows: particle acceleration and disc structure

Hot, tenuous advection-dominated accretion flows around black holes are ideal sites for the Fermi acceleration of relativistic particles at standing shock waves in the accretion disc. Previous work has demonstrated that the shock-acceleration process can be efficient enough to power the observed, strong outflows in radio-loud active galaxies such as M87. However, the dynamical effect (back-reaction) on the flow, exerted by the pressure of the relativistic particles, has not been previously considered, and this effect can have a significant influence on the disc structure. We reexamine the problem by developing a new, two-fluid model for the structure of the accretion disc that includes the dynamical effect of the relativistic particle pressure, combined with the pressure of the background (thermal) gas. The new model is analogous to the two-fluid model of cosmic ray acceleration in supernova-driven shock waves. As part of the model, we also develop a new set of shock jump conditions, which are solved along with the hydrodynamic conservation equations to determine the structure of the accretion disc. The solutions include the formation of a mildly relativistic outflow (jet) at the shock radius, driven by the relativistic particles accelerated in the disc. One of our main conclusions is that in the context of the new two-fluid accretion model, global smooth (shock-free) solutions do not exist, and the disc must always contain a standing shock wave, at least in the inviscid case considered here.

Gas and stellar spiral arms and their offsets in the grand-design spiral galaxy M51

Theoretical studies on the response of interstellar gas to a gravitational potential disc with a quasi-stationary spiral arm pattern suggest that the gas experiences a sudden compression due to standing shock waves at spiral arms. This mechanism, called a galactic shock wave, predicts that gas spiral arms move from downstream to upstream of stellar arms with increasing radius inside a corotation radius. In order to investigate if this mechanism is at work in the grand-design spiral galaxy M51, we have measured azimuthal offsets between the peaks of stellar mass and gas mass distributions in its two spiral arms. The stellar mass distribution is created by the spatially resolved spectral energy distribution fitting to optical and near infrared images, while the gas mass distribution is obtained by high-resolution CO and HI data. For the inner region (r < 150"), we find that one arm is consistent with the galactic shock while the other is not. For the outer region, results are less certain due to the narrower range of offset values, the weakness of stellar arms, and the smaller number of successful offset measurements. The results suggest that the nature of two inner spiral arms are different, which is likely due to an interaction with the companion galaxy.

Oscillations of a standing shock wave generated by the Richtmyer-Meshkov instability

Careful selection of a Mach number in a shock tube can produce a standing reflected shock wave. Its perturbed density/pressure discontinuities vary with time but otherwise are fixed in space, greatly facilitating their measurement.

CRITICAL SURFACE FOR EXPLOSIONS OF ROTATIONAL CORE-COLLAPSE SUPERNOVAE

The effect of rotation on the explosion of core-collapse supernovae is investigated systematically in three-dimensional simulations. In order to obtain the critical conditions for explosion as a function of mass accretion rate, neutrino luminosity, and specific angular momentum, rigidly rotating matter was injected from the outer boundary with an angular momentum, which is increased every 500 ms. It is found that there is a critical value of the specific angular momentum, above which the standing shock wave revives, for a given combination of mass accretion rate and neutrino luminosity, i.e. an explosion can occur by rotation even if the neutrino luminosity is lower than the critical value for a given mass accretion rate in non-rotational models. The coupling of rotation and hydrodynamical instabilities plays an important role to characterize the dynamics of shock revival for the range of specific angular momentum that are supposed to be realistic. Contrary to expectations from past studies, the most rapidly expanding direction of the shock wave is not aligned with the rotation axis. Being perpendicular to the rotation axis on average, it can be oriented in various directions. Its dispersion is small when the spiral mode of the standing accretion shock instability (SASI) governs the dynamics, while it is large when neutrino-driven convection is dominant. As a result of the comparison between 2D and 3D rotational models, it is found that m=!0 modes of neutrino-driven convection or SASI are important for shock revival around the critical surface.

Internal energy relaxation in shock wave structure

The Wang Chang-Uhlenbeck (WCU) equation is numerically integrated to characterize the internal structure of Mach 3 and Mach 5 shock waves in a gas with excitation in the internal energy states for the treatment of inelastic collisions. Elastic collisions are modeled with the hard sphere collision model and the transition rates for the inelastic collisions modified appropriately using probabilities based on relative velocities of the colliding particles. The collision integral is evaluated by the conservative discrete ordinate method [F. Tcheremissine, “Solution of the Boltzmann kinetic equation for high-speed flows,” Comput. Math. Math. Phys. 46, 315–329 (2006); F. Cheremisin, “Solution of the Wang Chang-Uhlenbeck equation,” Dokl. Phys. 47, 487–490 (2002)] developed for the Boltzmann equation. For the treatment of the diatomic molecules, the internal energy modes in the Boltzmann equation are described quantum mechanically given by the WCU equation. As a first step in the treatment of the inelastic collisions by the WCU equation, a two- and three-quantum system is considered to study the effect of the varying of (1) the inelastic cross section and (2) the energy gap between the quantum energy states. An alternative method, the direct simulation Monte Carlo method, is used for the Mach 3 shock wave to ensure the consistency of implementation in the two methods and there is an excellent agreement between the two methods. The results from the WCU implementation showed consistent trends for the Mach 3 and Mach5 standing shock waves simulations. Inelastic contributions change the downstream equilibrium state and allow the flow to transition to the equilibrium state further upstream.

Effect of the flow composition on outflow rates from accretion discs around black holes

We studied the outflow behaviour from accretion discs around black holes taking into account the vertical equilibrium accretion flow model. The outflow rate is found to depend crucially on flow composition. Our approach is to study the outflow behaviour as function of inflow around black holes with an equation of state which allows flow to be thermally relativistic close to black holes and non relativistic far away from black holes. We studied shock ejection model. A pure electron positron pair flow never undergoes shock transition while presence of some baryons (common in outflows and jets) makes it possible to have standing shock waves in the flow. It can be concluded that the presence of protons is necessary for the flow to show the outflow behaviour. The outflow rate is maximum when the flow contains the proton number density which is 27% of the electron number density. We conclude that a pure electron-positron jet is unlikely to form.

Catching the radio flare in CTA 102

The temporal and spatial spectral evolution of the jets of AGN can be studied with multi-frequency, multi-epoch VLBI observations. The combination of both, morphological and spectral parameters can be used to derive source intrinsic physical properties such as the magnetic field and the non-thermal particle density. In the first two papers of this series, we analyzed the single-dish light curves and the VLBI kinematics of the blazar CTA 102 and suggested a shock-shock interaction between a traveling and a standing shock wave as a possible scenario to explain the observed evolution of the component associated to the 2006 flare. In this paper we investigate the core-shift and spectral evolution to test our hypothesis of a shock-shock interaction. We used 8 multi-frequency VLBA observations to analyze the temporal and spatial evolution of the spectral parameters during the flare. We observed CTA 102 between May 2005 and April 2007 using the VLBA at six different frequencies spanning from 2 - 86 GHz. After the calibrated VLBA images were corrected for opacity, we performed a detailed spectral analysis. From the derived values we estimated the magnetic field and the density of the relativistic particles. The detailed analysis of the opacity shift reveals that the position of the jet core is proportional to nu^-1 with some temporal variations. The value suggests possible equipartition between magnetic field energy and particle kinetic energy densities at the most compact regions. From the variation of the physical parameters we deduced that the 2006 flare in CTA 102 is connected to the ejection of a new traveling feature (t=2005.9) and the interaction between this shock wave and a stationary structure around 0.1 mas from the core. The source kinematics together with the spectral and structural variations can be described by helical motions in an over-pressured jet.