Shock Dissipation Research Articles

Gaseous spiral structure and mass drift in spiral galaxies

We use hydrodynamic simulations to investigate nonlinear gas responses to an imposed stellar spiral potential in disk galaxies. The gaseous medium is assumed to be infinitesimally thin, isothermal, and unmagnetized. We consider various spiral-arm models with differing strength and pattern speed. We find that the extent and shapes of gaseous arms as well as the related mass drift rate depend rather sensitively on the arm pattern speed. In models where the arm pattern is rotating slow, the gaseous arms extend across the corotation resonance (CR) all the way to the outer boundary, with a pitch angle slightly smaller than that of the stellar counterpart. In models with a fast rotating pattern, on the other hand, spiral shocks are much more tightly wound than the stellar arms, and cease to exist in the regions near and outside the CR where $\mathcal{M}_\perp/{\rm sin} p_* \ge 25-40$, with $\mathcal{M}_\perp$ denoting the perpendicular Mach number of a rotating gas relative to the arms with pitch angle $p_*$. Inside the CR, the arms drive mass inflows at a rate of $\sim 0.05-3.0 {\rm M}_\odot {\rm yr}^{-1}$ to the central region, with larger values corresponding to stronger and slower arms. The contribution of the shock dissipation, external torque, and self-gravitational torque to the mass inflow is roughly 50%, 40%, and 10%, respectively. We demonstrate that the distributions of line-of-sight velocities and spiral-arm densities can be a useful diagnostic tool to distinguish if the spiral pattern is rotating fast or slow.

Shock Waves in Weakly Compressed Granular Media

We experimentally probe nonlinear wave propagation in weakly compressed granular media and observe a crossover from quasilinear sound waves at low impact to shock waves at high impact. We show that this crossover impact grows with the confining pressure P0, whereas the shock wave speed is independent of P0-two hallmarks of granular shocks predicted recently. The shocks exhibit surprising power law attenuation, which we model with a logarithmic law implying that shock dissipation is weak and qualitatively different from other granular dissipation mechanisms. We show that elastic and potential energy balance in the leading part of the shocks.

Dissipative ion-acoustic solitary and shock waves in a plasma with superthermal electrons

The excitation of a nonlinear ion-acoustic (IA) wave packet in a viscous plasma consisting of superthermal electrons and cold ions is investigated. It is assumed that the superthermal components obey the Kappa distribution. The standard reductive perturbation technique is employed to obtain a cubic complex Ginzburg–Landau type equation, which governs the dynamics of the amplitude of IA wave packets in a viscous plasma. In a weakly dissipative regime, by means of a perturbation method adopted from non-integrable dynamical systems theory, explicit soliton solutions are obtained of the dissipative dynamical system, determined as fixed points of a two-dimensional system of evolution equations describing the soliton amplitude and velocity. The stability of bright solitons is addressed using adiabatic perturbation theory in a weakly dissipative case. In a general dissipation regime, a novel type of travelling solitary (dissipative solitons) and shock-type solutions are derived for an envelope equation. Moreover, the dependence of the solitary and shock wave characteristics on relevant physical parameters of the problem is studied. It is shown that dissipative solitons do exist, sustained by a mutual balance between loss and gain terms, in addition to the interplay between dispersion and nonlinearity. The dependence of solitary and shock wave velocities on the parameters of the system are investigated. To feature distinctive characteristics of a dissipative soliton, it is compared with the bright soliton solution of the nonlinear Schrödinger equation.

Numerical investigation of the aerodynamic performance affected by spiral inlet and outlet in a positive displacement blower

The flow in the positive displacement blower is very complex. The existing two-dimensional numerical simulation cannot provide the detailed flow information, especially flow characteristics along the axial direction, which is unfavorable to improve the performance of positive displacement blower. To investigate the effects of spiral inlet and outlet on the aerodynamic performance of positive displacement blower, three-dimensional unsteady flow characteristics in a three-lobe positive displacement blower with and without the spiral inlet and outlet are simulated by solving Navier-Stokes equations coupled with RNG k-ɛ turbulent model. In the numerical simulation, the dynamic mesh technique and overset mesh updating method are used. The computational results are compared with the experimental measurements on the variation of flow rate with the outlet pressure to verify the validity of the numerical method presented. The results show that the mass flow rate with the change of pressure is slightly affected by the application of spiral inlet and outlet, but the internal flow state is largely affected. In the exhaust region, the fluctuations of pressure, velocity and temperature as well as the average values of velocity are significantly reduced. This illustrates that the spiral outlet can effectively suppress the fluctuations of pressure, thus reducing reflux shock and energy dissipation. In the intake area, the average value of pressure, velocity and temperature are slightly declined, but the fluctuations of them are significantly reduced, indicating that the spiral inlet plays the role in making the flow more stable. The numerical results obtained reveal the three-dimensional flow characteristics of the positive displacement blower with spiral inlet and outlet, and provide useful reference to improve performance and empirical correction in the noise-reduction design of the positive displacement blowers.

GRB 090727 AND GAMMA-RAY BURSTS WITH EARLY-TIME OPTICAL EMISSION

We present a multi-wavelength analysis of gamma-ray burst GRB 090727, for which optical emission was detected during the prompt gamma-ray emission by the 2-m autonomous robotic Liverpool Telescope and subsequently monitored for a further two days with the Liverpool and Faulkes telescopes. Within the context of the standard fireball model, we rule out a reverse shock origin for the early time optical emission in GRB 090727 and instead conclude that the early time optical flash likely corresponds to emission from an internal dissipation processes. Putting GRB 090727 into a broader observational and theoretical context, we build a sample of 36 gamma-ray bursts (GRBs) with contemporaneous early time optical and gamma-ray detections. From these GRBs, we extract a sub-sample of 18 GRBs, which show optical peaks during prompt gamma-ray emission, and perform detailed temporal and spectral analysis in gamma-ray, X-ray, and optical bands. We find that in most cases early time optical emission shows sharp and steep behaviour, and notice a rich diversity of spectral properties. Using a simple internal shock dissipation model, we show that the emission during prompt GRB phase can occur at very different frequencies via synchrotron radiation. Based on the results obtained from observations and simulation, we conclude that the standard external shock interpretation for early time optical emission is disfavoured in most cases due to sharp peaks ($\Delta t/t < 1$) and steep rise/decay indices, and that internal dissipation can explain the properties of GRBs with optical peaks during gamma-ray emission.

Fermionic shock waves: Distinguishing dissipative versus dispersive regularizations

The collision of two clouds of Fermi gas at unitarity (UFG) has been recently observed to lead to shock waves whose regularization mechanism, dissipative or dispersive, is being debated. While classical, dissipative shocks, as in gas dynamics, develop a steep, localized shock front that translates at a well-defined speed, dispersively regularized shocks are distinguished by an expanding region of short wavelength oscillations with two speeds, those of the leading and trailing edges. For typical UFG experimental conditions, the theoretical oscillation length scale is smaller than the resolution of present imaging systems so it is unclear how to determine the shock type from its structure alone. Two experimental methods to determine the appropriate regularization mechanism are proposed: measurement of the shock speed and observation of a one-dimensional collision experiment with sufficiently tight radial confinement.

Nonlinear phenomena related to the solar shock motion in the Earth’s magnetosphere

The motion of the MHD nonlinear shock in the Earth’s magnetosphere is considered in the scope of magnetic hydrodynamics. This wave comes from the solar wind and is refracted into the magnetosphere, generating a fast return rarefaction wave. It has been indicated that a wave refracted into the magnetosphere is a weak fast dissipative shock, propagating in magnetospheric plasma at a velocity higher than its propagation velocity in a solar wind stream. The wave motion near the Earth-Sun line with regard to the effect of the geomagnetic field transverse component is described. In this case, shock damping follows the generalized Crussard-Landau law and a wave retains its shock character up to the plasmapause, interacting with this region when an arbitrary MHD discontinuity is disintegrated. It is stated that an MHD shock loses its shock character when moving in a strongly inhomogeneous plasma within the plasmasphere and a weak shock reflected from the plasmapause can combine with a return secondary shock in the magnetosheath, promoting the experimentally observed backward motion of the bow shock front.

ANGULAR MOMENTUM TRANSPORT BY ACOUSTIC MODES GENERATED IN THE BOUNDARY LAYER. II. MAGNETOHYDRODYNAMIC SIMULATIONS

We perform global unstratified 3D magnetohydrodynamic simulations of an astrophysical boundary layer (BL) -- an interface region between an accretion disk and a weakly magnetized accreting object such as a white dwarf -- with the goal of understanding the effects of magnetic field on the BL. We use cylindrical coordinates with an isothermal equation of state and investigate a number of initial field geometries including toroidal, vertical, and vertical with zero net flux. Our initial setup consists of a Keplerian disk attached to a non-rotating star. In a previous work, we found that in hydrodynamical simulations, sound waves excited by shear in the BL were able to efficiently transport angular momentum and drive mass accretion onto the star. Here we confirm that in MHD simulations, waves serve as an efficient means of angular momentum transport in the vicinity of the BL, despite the magnetorotational instability (MRI) operating in the disk. In particular, the angular momentum current due to waves is at times larger than the angular momentum current due to MRI. Our results suggest that angular momentum transport in the BL and its vicinity is a global phenomenon occurring through dissipation of waves and shocks. This point of view is quite different from the standard picture of transport by a local anomalous turbulent viscosity. In addition to angular momentum transport, we also study magnetic field amplification within the BL. We find that the field is indeed amplified in the BL, but only by a factor of a few and remains subthermal.

Changes in MR relaxation times of the meniscal body with loading: an in vivo pilot study in knee osteoarthritis

Purpose: The meniscus, a fibrocartilaginous tissue found within the knee joint, is responsible for joint congruity, shock dissipation, load transmission, lubrication, and stability of the joint. The meniscus is increasingly being recognized as an important tissue in knee osteoarthritis (OA). Recent studies have shown the potential of magnetic resonance (MR) relaxation times (T1r and T2) in studying biochemical composition of meniscus and therefore they may play a role in quantifying early meniscal degeneration and injury. One central function of themenisci is load transmission and studying the effect of acute loading on the meniscal T1r and T2 values may provide insight into the development of joint degeneration. Thus the purpose of this study is to prospectively compare changes in T1r and T2 in the meniscal body with acute loading in knees with OA and with those of age-matched healthy control menisci. Methods: Female subjects (age: 40-70 years, BMI: 20-35 kg/m2) with (KL score of 2 or 3, n 1⁄420) and without (KL score of 0, n1⁄410) radiographic evidence of knee OA, were imaged on a 3T GEMR scanner using a custommade loading device. MR images (Coronal SPGR and T1r and T2 mapping sequences) were acquired with the knee flexed at 20 with and without a compressive load of 50% of the subject's bodyweight (Figure 1) using established pulse sequences. The regions of interest (ROIs) for quantifying T1r and T2 values in the meniscus body were defined on the coronal SPGR images and superimposed over relaxation time maps. Anterior and posterior horns were not evaluated due to substantial partial volume effects in coronal images. Three different zones (outer, middle, and inner) of meniscus were defined by dividing the meniscus ROIs into three different parts with each part occupying one-third the width of the meniscus (Figure 2). After adjusting for age and BMI in the general linear regression model, repeated measures ANOVAwas used to detect significant differences in T1r and T2 with and without loading. Results: The average T1r and T2 values in all zones were significantly higher in OA patients compared with controls in unloaded condition, but not in loaded condition (Figure 3 and Figure 4). ΔT1r and ΔT2 in the outer zone of the medial meniscus in controls was significantly higher than the OA subjects (14.8% vs. 6.6%, P1⁄40.046 for ΔT1r, and 15.7% vs. 5.8%, P1⁄40.027 for ΔT2). In other zones (middle and inner), the same trend was observed but did not reach significance. Pooled data showed, significant increase in T1r of the outer zone of both medial (9.1%, P<0.0001) and lateral (6.8%, P1⁄40.014) meniscus body was observed with loading. Whereas, significant increase in T2 was observed in the outer zone of the medial meniscus (8.4%, P1⁄4 0.0003) only with minimal changes in the lateral meniscus (2.6%, P1⁄40.221). Conclusions: Elevated T1r and T2 in subjects with OA in the unloaded condition agree with literature and suggest that relaxation times of the menisci may have value in monitoring early disease. Significant relaxation time elevations in the outer portion of the meniscus with acute loading in both groupsmay reflect tissue hydration changes as the inner and middle portions of the meniscus bear load. The observation that Abstracts / Osteoarthritis an

Spontaneous hot flow anomalies at quasi‐parallel shocks: 2. Hybrid simulations

AbstractMotivated by recent THEMIS observations, this paper uses 2.5‐D electromagnetic hybrid simulations to investigate the formation of Spontaneous Hot Flow Anomalies (SHFAs) upstream of quasi‐parallel bow shocks during steady solar wind conditions and in the absence of discontinuities. The results show the formation of a large number of structures along and upstream of the quasi‐parallel bow shock. Their outer edges exhibit density and magnetic field enhancements, while their cores exhibit drops in density, magnetic field, solar wind velocity, and enhancements in ion temperature. Using virtual spacecraft in the simulation, we show that the signatures of these structures in the time series data are very similar to those of SHFAs seen in THEMIS data and conclude that they correspond to SHFAs. Examination of the simulation data shows that SHFAs form as the result of foreshock cavitons interacting with the bow shock. Foreshock cavitons in turn form due to the nonlinear evolution of ULF waves generated by the interaction of the solar wind with the backstreaming ions. Because foreshock cavitons are an inherent part of the shock dissipation process, the formation of SHFAs is also an inherent part of the dissipation process leading to a highly nonuniform plasma in the quasi‐parallel magnetosheath including large‐scale density and magnetic field cavities.

HELIOSPHERIC STRUCTURE: THE BOW WAVE AND THE HYDROGEN WALL

Recent IBEX observations indicate that the local interstellar medium (LISM) flow speed is less than previously thought (23.2 km s–1 rather than 26 km s–1). Reasonable LISM plasma parameters indicate that the LISM flow may be either marginally super-fast magnetosonic or sub-fast magnetosonic. This raises two challenging questions: (1) Can a LISM model that is barely super-fast or sub-fast magnetosonic account for Lyα observations that rely critically on the additional absorption provided by the hydrogen wall (H-wall)? and (2) If the LISM flow is weakly super-fast magnetosonic, does the transition assume the form of a traditional shock or does neutral hydrogen (H) mediate shock dissipation and hence structure through charge exchange? Both questions are addressed using three three-dimensional self-consistently coupled magnetohydrodynamic plasma—kinetic H models with different LISM magnetic field strengths (2, 3, and 4 μG) as well as plasma and neutral H number densities. The 2 and 3 μG models are fast magnetosonic far upwind of the heliopause whereas the 4 μG model is fully subsonic. The 2 μG model admits a broad (~50-75 AU) bow-shock-like structure. The 3 μG model has a smooth super-fast-sub-fast magnetosonic transition that resembles a very broad, ~200 AU thick, bow wave. A theoretical analysis shows that the transition from a super-fast to a sub-fast magnetosonic downstream state is due to the charge exchange of fast neutral H and hot neutral H created in the supersonic solar wind and hot inner heliosheath, respectively. For both the 2 μG and the 3 μG models, the super-fast magnetosonic LISM flow passes through a critical point located where the fast magnetosonic Mach number M = 1 and Qe = γ/(γ – 1)UQm , where Qe and Qm are the plasma energy and momentum source terms due to charge exchange, U is the LISM flow speed, and γ is the plasma adiabatic index. Because the Mach number is only barely super-fast magnetosonic in the 3 μG case, the hot and fast neutral H can completely mediate the transition and impose a charge exchange length scale on the structure, making the solar-wind-LISM interaction effectively bow-shock-free. The charge exchange of fast and hot heliospheric neutral H therefore provides a primary dissipation mechanism at the weak heliospheric bow shock, in some cases effectively creating a one-shock heliosphere (i.e., a heliospheric termination shock only). Both super-fast magnetosonic models produce a sizeable H-wall. We find that (1) a sub-fast magnetosonic LISM flow cannot model the observed Lyα absorption profiles along the four sightlines considered (α Cen, 36 Oph, DK UMa, and χ1 Ori—upwind, sidewind, and downwind respectively); (2) both the super-fast magnetosonic models can account for the Lyα observations, with possibly the bow-shock-free 3 μG model being slightly favored. Subject to further modeling and comparison against further lines of sight, we conclude with the tantalizing possibility that IBEX may have discovered a class of interstellar shocks mediated by neutral H.

Internal shocks at the origin of the flat spectral energy distribution of compact jets

Abstract An internal shock model is proposed to interpret the radio to infrared (IR) emission of the compact jets observed in the hard spectral state of X-ray binaries. Assuming that the specific bulk Lorentz factor of the jet at its base varies with a flicker noise power spectrum [i.e. P(f) ∝ 1/f], we estimate the energy dissipation profile along the jet and the resulting partially self-absorbed synchrotron emission. For this type of velocity fluctuations, and a conical jet geometry, the shock dissipation at large distance from the black hole balances exactly the adiabatic losses. This leads to a flat radio to IR spectral energy distribution similar to that observed in compact jets.

Phase slips and dissipation of Alfvenic intermediate shocks and solitons

The time evolution of a rotational discontinuity, characterized by a change of the magnetic-field direction by an angle Δθ such that π&amp;lt;|Δθ|&amp;lt;2π and no amplitude variation, is considered in the framework of asymptotic models that, through reductive perturbative expansions, isolate the dynamics of parallel or quasi-parallel Alfvén waves. In the presence of viscous and Ohmic dissipation, and for a zero or sufficiently weak dispersion (originating from the Hall effect), an intermediate shock rapidly forms, steepens and undergoes reconnection through a quasi gradient collapse, leading to a reduction of |Δθ| by an amount of 2π, which can be viewed as the breaking of a topological constraint. Afterwards, as |Δθ|&amp;lt;π, the intermediate shock broadens and slowly dissipates. In the case of a phase jump |Δθ|&amp;gt;3π, which corresponds to a wave train limited on both sides by uniform fields, a sequence of such reconnection processes takes place. Differently, in the presence of a strong enough dispersion, the rotational discontinuity evolves, depending on the sign of Δθ, to a dark or bright soliton displaying a 2π phase variation. The latter is then eliminated, directly by reconnection in the case of a dark soliton, or through a more complex process involving a quasi amplitude collapse in that of a bright soliton. Afterwards, the resulting structure is progressively damped. For a prescribed initial rotational discontinuity, both quasi gradient and amplitude collapses lead to a sizeable energy decay that in the collisional regime is independent of the diffusion coefficient η but requires a time scaling like 1/η. In the non-collisional regime where dissipation originates from Landau resonance, the amount of dissipated energy during the event is independent of the plasma β, but the process becomes slower for smaller β.

Weibel-Instability-Mediated Collisionless Shocks in the Laboratory with Ultraintense Lasers

The formation of nonrelativistic collisionless shocks in the laboratory with ultrahigh intensity lasers is studied via abinitio multidimensional particle-in-cell simulations. The microphysics behind shock formation and dissipation and the detailed shock structure are analyzed, illustrating that the Weibel instability plays a crucial role in the generation of strong subequipartition magnetic fields that isotropize the incoming flow and lead to the formation of a collisionless shock, similar to what occurs in astrophysical scenarios. The possibility of generating such collisionless shocks in the laboratory opens the way to the direct study of the physics associated with astrophysical shocks.

Discovery of interstellar mercapto radicals (SH) with the GREAT instrument on SOFIA

We report the first detection of interstellar mercapto radicals, obtained along the sight-line to the submillimeter continuum source W49N. We have used the GREAT instrument on SOFIA to observe the 1383 GHz Doublet Pi 3/2 J = 5/2 - 3/2 lambda doublet in the upper sideband of the L1 receiver. The resultant spectrum reveals SH absorption in material local to W49N, as well as in foreground gas, unassociated with W49N, that is located along the sight-line. For the foreground material at velocities in the range 37 - 44 km/s with respect to the local standard of rest, we infer a total SH column density ~ 2.6 E+12 cm-2, corresponding to an abundance of ~ 7 E-9 relative to H2, and yielding an SH/H2S abundance ratio ~ 0.13. The observed SH/H2S abundance ratio is much smaller than that predicted by standard models for the production of SH and H2S in turbulent dissipation regions and shocks, and suggests that the endothermic neutral-neutral reaction SH + H2 -> H2S + H must be enhanced along with the ion-neutral reactions believed to produce CH+ and SH+ in diffuse molecular clouds.

THE EFFECTS OF IRRADIATION ON HOT JOVIAN ATMOSPHERES: HEAT REDISTRIBUTION AND ENERGY DISSIPATION

Hot Jupiters, due to the proximity to their parent stars, are subjected to a strong irradiating flux which governs their radiative and dynamical properties. We compute a suite of 3D circulation models with dual-band radiative transfer, exploring a relevant range of irradiation temperatures, both with and without temperature inversions. We find that, for irradiation temperatures T \lesssim 2000 K, heat redistribution is very efficient, producing comparable day- and night-side fluxes. For Tirr \approx 2200-2400 K, the redistribution starts to break down, resulting in a high day-night flux contrast. Our simulations indicate that the efficiency of redistribution is primarily governed by the ratio of advective to radiative timescales. Models with temperature inversions display a higher day-night contrast due to the deposition of starlight at higher altitudes, but we find this opacity-driven effect to be secondary compared to the effects of irradiation. The hotspot offset from the substellar point is large when insolation is weak and redistribution is efficient, and decreases as redistribution breaks down. The atmospheric flow can be potentially subjected to the Kelvin-Helmholtz instability (as indicated by the Richardson number) only in the uppermost layers, with a depth that penetrates down to pressures of a few millibars at most. Shocks penetrate deeper, down to several bars in the hottest model. Ohmic dissipation generally occurs down to deeper levels than shock dissipation (to tens of bars), but the penetration depth varies with the atmospheric opacity. The total dissipated Ohmic power increases steeply with the strength of the irradiating flux and the dissipation depth recedes into the atmosphere, favoring radius inflation in the most irradiated objects.

Viscoelastic Properties and Shock Response of Coarse-Grained Models of Multiblock versus Diblock Copolymers: Insights into Dissipative Properties of Polyurea

We compare and contrast the microstructure, viscoelastic properties, and shock response of coarse-grained models of multiblock copolymer and diblock copolymers using molecular dynamics simulations. This study is motivated by the excellent dissipative and shock-mitigating properties of polyurea, speculated to arise from its multiblock chain architecture. Our microstructural analyses reveal that the multiblock copolymer microphase-separates into small, interconnected, rod-shaped, hard domains surrounded by a soft matrix, whereas the diblock copolymer forms larger, unconnected, hard domains. Our viscoelastic analyses indicate that compared with the diblock copolymer, the multiblock copolymer is not only more elastic but also more dissipative, as signified by its larger storage and loss modulus at low to intermediate frequencies. Our shock simulations and slip analyses reveal that shock waves propagate slower in the multiblock copolymer in comparison with the diblock copolymer, most likely due to the more deformable hard domains in the former system. These results suggest that the multiblock architecture of polyurea might impart polyurea with smaller, more deformable, and interconnected hard domains that lead to improved energy dissipation and lower shock speeds.

Shock dissipation in magnetically dominated impulsive flows

The idea that cosmic relativistic jets are magnetically driven Poynting-dominated flows has many attractive features but also some problems. One of them is the low efficiency of shock dissipation in highly magnetized plasma. Indeed, the observations of gamma-ray bursts (GRBs) and their afterglow emission indicate very high radiative efficiency of relativistic jets associated with these phenomena. We have revisited the issue of shock dissipation and emission and its implications for the internal shock model of the prompt GRB emission and studied it in the context of impulsive Poynting-dominated flows. Our results show that unless the magnetization of GRB jets is extremely high, σ > 100 in the prompt emission zone, the magnetic model may still be compatible with the observations. First, for σ≃ 1 the dissipation efficiency of fast magnetosonic shock is still quite high, ∼30 per cent. Secondly, the main effect of reduced dissipation efficiency is merely an increase in the size of the dissipation zone, and even for highly magnetized GRB jets, this size may remain below the external shock radius, provided the central engine can emit magnetic shells on the time-scale well below the typical observed variability scale of 1 s. Our analytical and numerical results suggest that strong interaction between shells begins not during the coasting phase but well before it. As the result, the impulsive jet in the dissipation zone is best described not as a collection of shells but as a continuous highly magnetized flow with a high amplitude magnetosonic wave component. How exactly the dissipated wave energy is distributed between the radiation and the bulk kinetic energy of radial jets depends on the relative rates of radiative and adiabatic cooling. In the fast radiative cooling regime, the corresponding radiative efficiency can be as high as the wave contribution to their energy budget, independently of the magnetization. Moreover, after leaving the zone of prompt emission, the jet may still remain Poynting dominated, leading to weaker emission from the reverse shock compared to non-magnetic models. Energetically subdominant weakly magnetized ‘clouds’ in otherwise strongly magnetized jets may significantly increase the overall efficiency of the shock dissipation.

Numerical convergence in self-gravitating shearing sheet simulations and the stochastic nature of disc fragmentation

We study numerical convergence in local two-dimensional hydrodynamical simulations of self-gravitating accretion discs with a simple cooling law. It is well-known that there exists a steady gravito-turbulent state, in which cooling is balanced by dissipation of weak shocks, with a net outward transport of angular momentum. Previous results indicated that if cooling is too fast (typical time scale 3/Omega, where Omega is the local angular velocity), this steady state can not be maintained and the disc will fragment into gravitationally bound clumps. We show that, in the two-dimensional local approximation, this result is in fact not converged with respect to numerical resolution and longer time integration. Irrespective of the cooling time scale, gravito-turbulence consists of density waves as well as transient clumps. These clumps will contract because of the imposed cooling, and collapse into bound objects if they can survive for long enough. Since heating by shocks is very local, the destruction of clumps is a stochastic process. High numerical resolution and long integration times are needed to capture this behaviour. We have observed fragmentation for cooling times up to 20/Omega, almost a factor 7 higher than in previous simulations. Fully three-dimensional simulations with a more realistic cooling prescription are necessary to determine the effects of the use of the two-dimensional approximation and a simple cooling law.

On the nature of the parameter space in the presence of dissipative standing shocks in accretion flows around black holes

The spectral properties of black hole candidates and outflow rates depend crucially on the models of accretion flow, and thus they are interconnected. In a model of transonic flow, the centrifugal barrier forms a shock wave in the accretion disc at a few tens of Schwarzschild radii. The post-shock region (i.e. the region between the shock and the innermost critical point) can act as a Compton cloud as well a reservoir of outgoing jets/outflows. In order to compute the parameter space in which the outflow can form, we use a suitable Mach number relation that can be satisfied at the shock derived in our earlier work in the presence of dissipation and outflows. Assuming three models of accretion flow (i.e. models of vertical equilibrium, conical wedge shape and constant height), we examine the parameter space of the specific energy and the specific angular momentum for dissipative shock with mass loss. In the first two models, we find that the parameter space is reduced as the cooling rate is increased. However, in the case of the constant height model, the parameter space initially increases with the cooling process, but starts to decrease with a further increase in cooling. One common property in all three accretion flow models is that, above a critical amount of cooling, the parameter space disappears completely. This indicates that the spectrally soft states might not have a significant amount of outflows from the accretion disc.