Dynamic evolution of a quasi-spherical general polytropic magnetofluid with self-gravity

In various astrophysical contexts, we analyze self-similar behaviours of magnetohydrodynamic (MHD) evolution of a quasi-spherical polytropic magnetized gas under self-gravity with the specific entropy conserved along streamlines. In particular, this MHD model analysis frees the scaling parameter n in the conventional polytropic self-similar transformation from the constraint of n+γ=2 with γ being the polytropic index and therefore substantially generalizes earlier analysis results on polytropic gas dynamics that has a constant specific entropy everywhere in space at all time. On the basis of the self-similar nonlinear MHD ordinary differential equations, we examine behaviours of the magnetosonic critical curves, the MHD shock conditions, and various asymptotic solutions. We then construct global semi-complete self-similar MHD solutions using a combination of analytical and numerical means and indicate plausible astrophysical applications of these magnetized flow solutions with or without MHD shocks.     

Jet simulations extending radially self-similar magnetohydrodynamics models

We perform a numerical simulation of magnetohydrodynamics (MHD) radially self-similar jets, whose prototype is the Blandford & Payne analytical example. The final steady state that is reached is valid close to the rotation axis and also at large distances above the disc where the classical analytical model fails to provide physically acceptable solutions. The outflow starts with a subslow magnetosonic speed, which subsequently crosses all relevant MHD critical points and corresponding magnetosonic separatrix surfaces. The characteristics are plotted together with the Mach cones and the superfast magnetosonic outflow satisfies MHD causality. The final solution remains close enough to the analytical one, which is thus shown to be topologically stable and robust for various boundary conditions.     

Steady and Time-Dependent MHD Modelling of Jets

A brief review is given of some results of our work on the construction of (I) steady and (II) time-dependent MHD models for nonrelativistic and relativistic astrophysical outflows and jets, analytically and numerically. The only available exact solutions for MHD outflows are those in separable coordinates, i.e., with the symmetry of radial or meridional self-similarity. Physically accepted solutions pass from the fast magnetosonic separatrix surface in order to satisfy MHD causality. An energetic criterion is outlined for selecting radially expanding winds from cylindrically expanding jets. Numerical simulations of magnetic self-collimation verify the conclusions of analytical steady solutions. We also propose a two-component model consisting of a wind outflow from a central object and a faster rotating outflow launched from a surrounding accretion disk which plays the role of the flow collimator. We also discuss the problem of shock formation during the magnetic collimation of wind-type outflows into jets.     

Protostellar evolution during time-dependent anisotropic collapse

The formation and collapse of a protostar involves the simultaneous infall and outflow of material in the presence of magnetic fields, self-gravity and rotation. We use self-similar techniques to self-consistently model the anisotropic collapse and outflow by using a set of angle-separated self-similar equations. The outflow is quite strong in our model, with the velocity increasing in proportion to radius, and material formally escaping to infinity in the finite time is required for the central singularity to develop.
Analytically tractable collapse models have been limited mainly to spherically symmetric collapse, with neither magnetic field nor rotation. Other analyses usually employ extensive numerical simulations, or either perturbative or quasistatic techniques. Our model is unique as an exact solution to the non-stationary equations of self-gravitating magnetohydrodynamics (MHD), which features co-existing regions of infall and outflow.
The velocity and magnetic topology of our model is quadrupolar, although dipolar solutions may also exist. We provide a qualitative model for the origin and subsequent evolution of such a state. However, a central singularity forms at late times, and we expect the late-time behaviour to be dominated by the singularity, rather than depend on the details of its initial state. Our solution may, therefore, have the character of an attractor among a much more general class of self-similarity.     

Self-similar solution of hot accretion flows with ordered magnetic field and outflow

Observations and numerical magnetohydrodynamic (MHD) simulations indicate the existence of outflows and ordered large-scale magnetic fields in the inner region of hot accretion flows. In this paper, we present the self-similar solutions for advection-dominated accretion flows (ADAFs) with outflows and ordered magnetic fields. Stimulated by numerical simulations, we assume that the magnetic field has a strong toroidal component and a vertical component in addition to a stochastic component. We obtain the self-similar solutions to the equations describing the magnetized ADAFs, taking into account the dynamical effects of the outflow. We compare the results with the canonical ADAFs and find that the dynamical properties of ADAFs such as radial velocity, angular velocity and temperature can be significantly changed in the presence of ordered magnetic fields and outflows. The stronger the magnetic field is, the lower the temperature of the accretion flow will be and the faster the flow rotates. The relevance to observations is briefly discussed.     

Hot accretion with outflow and thermal conduction

We present self-similar solutions for advection-dominated accretion flows with thermal conduction in the presence of outflows. Possible effects of outflows on the accretion flow are parametrized and a saturated form of thermal conduction, as is appropriate for the weakly-collisional regime of interest, is included in our model. While the cooling effect of outflows is noticeable, thermal conduction provides an extra heating source. In comparison to accretion flows without winds, we show that the disc rotates faster and becomes cooler because of the angular momentum and energy flux which are taking away by the winds. But thermal conduction opposes the effects of winds and not only decreases the rotational velocity, but increases the temperature. However, reduction of the surface density and the enhanced accretion velocity are amplified by both of the winds and the thermal conduction. We find that for stronger outflows, a higher level of saturated thermal conduction is needed to significantly modify the physical profiles of the accretion flow.     

MHD Outflows from Hot Coronae

We discuss the application of meridionally self-similar models to winds and jets from hot coronae, in particular in the central region of accretion disks. A summary of how they may help understanding the evolution of jets from young stars is outlined. Then we discuss their application to the classification of AGN jets and extension to the relativistic regime of these exact axisymmetric solutions. Finally we discuss how it is possible to extend the polytropic equation of state and Parker winds to the relativistic regime to have a simple toy model for understanding thermal acceleration.     

Near-IR [Fe ii] Emission Diagnostics: Disk Winds in Young Stars

We investigate in this contribution emissivity properties of the [Fe ii] near-IR lines and their application to the study of jets in young stars. We report a model-independent method to determine the gas phase abundance in jets. Then, we present synthetic maps deduced from a recent self-consistent MHD cold disk wind model from which the thermal solution has been solved a posteriori. Kinematics is compared with observations in the [Fe ii] near-IR lines of L1551-IRS5. General kinematical behaviour is well reproduced, the existence of two velocity components in particular. However, we note a relative deficit in emission at intermediate velocity as observed in the jets from optically visible T Tauri stars. We examine predicted rotation signatures for various types of MHD disk winds. Compared to observations of DG Tau, warm disk winds reproduce quite well observed velocity shifts, whereas cold solutions predict too high toroidal velocities by a factor 2–3.     

Hot accretion flow with ordered magnetic field, outflow, and saturated conduction

The importance of thermal conduction on hot accretion flow is confirmed by observations of hot gas that surrounds Sgr A^? and a few other nearby galactic nuclei. On the other hand, the existence of outflow in accretion flows is confirmed by observations and magnetohydrodynamic (MHD) simulations. In this research, we study the influence of both thermal conduction and outflow on hot accretion flows with ordered magnetic field. Since the inner regions of hot accretion flows are, in many cases, collisionless with an electron mean free path due to Coulomb collision larger than the radius, we use a saturated form of thermal conduction, as is appropriate for weakly collisional systems. We also consider the influence of outflow on accretion flow as a sink for mass, and the radial and the angular momentum, and energy taken away from or deposited into the inflow by outflow. The magnetic field is assumed to have a toroidal component and a vertical component as well as a stochastic component. We use a radially self-similar method to solve the integrated equations that govern the behavior of such accretion flows. The solutions show that with an ordered magnetic field, both the surface density and the sound speed decrease, while the radial and angular velocities increase. We found that a hot accretion flow with thermal conduction rotates more quickly and accretes more slowly than that without thermal conduction. Moreover, thermal conduction reduces the influences of the ordered magnetic field on the angular velocities and the sound speed. The study of this model with the magnitude of outflow parameters implies that the gas temperature decreases due to mass, angular momentum, and energy loss. This property of outflow decreases for high thermal conduction.     

Self-similar dynamics of a magnetized polytropic gas

In broad astrophysical contexts of large-scale gravitational collapses and outflows and as a basis for various further astrophysical applications, we formulate and investigate a theoretical problem of self-similar magnetohydrodynamics (MHD) for a non-rotating polytropic gas of quasi-spherical symmetry permeated by a completely random magnetic field. Within this framework, we derive two coupled nonlinear MHD ordinary differential equations (ODEs), examine properties of the magnetosonic critical curve, obtain various asymptotic and global semi-complete similarity MHD solutions, and qualify the applicability of our results. Unique to a magnetized gas cloud, a novel asymptotic MHD solution for a collapsing core is established. Physically, the similarity MHD inflow towards the central dense core proceeds in characteristic manners before the gas material eventually encounters a strong radiating MHD shock upon impact onto the central compact object. Sufficiently far away from the central core region enshrouded by such an MHD shock, we derive regular asymptotic behaviours. We study asymptotic solution behaviours in the vicinity of the magnetosonic critical curve and determine smooth MHD eigensolutions across this curve. Numerically, we construct global semi-complete similarity MHD solutions that cross the magnetosonic critical curve zero, one, and two times. For comparison, counterpart solutions in the case of an isothermal unmagnetized and magnetized gas flows are demonstrated in the present MHD framework at nearly isothermal and weakly magnetized conditions. For a polytropic index γ=1.25 or a strong magnetic field, different solution behaviours emerge. With a strong magnetic field, there exist semi-complete similarity solutions crossing the magnetosonic critical curve only once, and the MHD counterpart of expansion-wave collapse solution disappears. Also in the polytropic case of γ=1.25, we no longer observe the trend in the speed-density phase diagram of finding infinitely many matches to establish global MHD solutions that cross the magnetosonic critical curve twice.      

Two-flow magnetohydrodynamical jets around young stellar objects

We present the first-ever simulations of non-ideal magnetohydrodynamical (MHD) stellar winds coupled with disc-driven jets where the resistive and viscous accretion disc is self-consistently described. The transmagnetosonic, collimated MHD outflows are investigated numerically using the VAC code. Our simulations show that the inner outflow is accelerated from the central object hot corona thanks to both the thermal pressure and the Lorentz force. In our framework, the thermal acceleration is sustained by the heating produced by the dissipated magnetic energy due to the turbulence. Conversely, the outflow launched from the resistive accretion disc is mainly accelerated by the magneto-centrifugal force. We also show that when a dense inner stellar wind occurs, the resulting disc-driven jet have a different structure, namely a magnetic structure where poloidal magnetic field lines are more inclined because of the pressure caused by the stellar wind. This modification leads to both an enhanced mass ejection rate in the disc-driven jet and a larger radial extension which is in better agreement with the observations besides being more consistent.     

A model for GRB jets

By using relativistic, axisymmetric, ideal MHD, we examine the motion of the baryon/e^±/ photon fluid that emanates from a stellar-mass compact object/debris-disk system (a common outcome of many progenitor models). We prove that the motion can be described as a frozen pulse, which permits the study of each shell of the pancake-shaped outflow using steady-state equations. The ejected energy flux is dominated by the electromagnetic (Poynting) contribution, but it can also have a non negligible e^±/radiation (thermal fireball)component. We demonstrate, through exact self-similar solutions, that the flow is first thermally and subsequently magnetically accelerated up to equipartition between kinetic and Poynting fluxes, i.e., ～ 50% of the total energy is converted into baryonic kinetic energy. The electromagnetic forces also collimate the flow, reaching a cylindrical structure asymptotically.     

Launching mechanisms of astrophysical jets

The combination of accretion disks and supersonic jets is used to model many active astrophysical objects, viz., young stars, relativistic stars, and active galactic nuclei. However, existing theories on the physical processes by which these structures transfer angular momentum and energy from disks to jets through viscous or magnetic torques are still relatively approximate. Global stationary solutions do not permit understanding the formation and stability of these structures; and global numerical simulations that include both the disk and jet physics are often limited to relatively short time scales and astrophysically out-of-range values of viscosity and resistivity parameters that are instead crucial to defining the coupling of the inflow/outflow dynamics. Along these lines we discuss self-consistent time-dependent simulations of the launching of supersonic jets by magnetized accretion disks, using high resolution numerical techniques. We shall concentrate on the effects of the disk physical parameters, and discuss under which conditions steady state solutions of the type proposed in the self-similar models of Blandford and Payne can be reached and maintained in a self-consistent nonlinear stationary state.     

The magnetic prandtl number on structure of hot and cold accretion flows

The aim of this work is to investigate the effect of the presence of a magnetic Prandtl number on the structure of an accretion flow with a bipolar outflow by focusing on the density structure. Two cold and hot classes are considered for accretion flows. According to the self-similar assumptions in the radial direction and boundary conditions as well, we solve the MHD equations along the θ-direction to obtain the density structure. In addition, we consider the results in two gas-pressure-dominated and radiation-pressure-dominated regions. The obtained results show that the existence of a magnetic prandtl number may lead to bump formation in hot accretion flows, which may have consequences for planet formation. Furthermore, some discontinuations in the density structure are seen at some regions resulting in the production of a gap in the case of cold accretion flows. The results of this work may be useful in the consideration of the Rossby wave instability in both classes of accretion flows.     

General polytropic magnetofluid under self-gravity: Voids and shocks

We study the self-similar magnetohydrodynamics (MHD) of a quasi-spherical expanding void (viz. cavity or bubble) surrounding the centre of a self-gravitating gas sphere with a general polytropic equation of state. We show various analytic asymptotic solutions near the void boundary in different parameter regimes and obtain the corresponding void solutions by extensive numerical explorations. We find novel void solutions of zero density on the void boundary. These new void solutions exist only in a general polytropic gas and feature shell-type density profiles. These void solutions, if not encountering the magnetosonic critical curve (MCC), generally approach the asymptotic expansion solution far from the central void with a velocity proportional to radial distance. We identify and examine free-expansion solutions, Einstein–de Sitter expansion solutions, and thermal-expansion solutions in three different parameter regimes. Under certain conditions, void solutions may cross the MCC either smoothly or by MHD shocks, and then merge into asymptotic solutions with finite velocity and density far from the centre. Our general polytropic MHD void solutions provide physical insight for void evolution, and may have astrophysical applications such as massive star collapses and explosions, shell-type supernova remnants and hot bubbles in the interstellar and intergalactic media, and planetary nebulae.     

Sunyaev–Zel'dovich profiles and scaling relations: modelling effects and observational biases

We use high-resolution hydrodynamic resimulations to investigate the properties of the thermal Sunyaev–Zel'dovich (SZ) effect from galaxy clusters. We compare results obtained using different physical models for the intracluster medium (ICM), and show how they modify the SZ emission in terms of cluster profiles and scaling relations. We also produce realistic mock observations to verify whether the results from hydrodynamic simulations can be confirmed. We find that SZ profiles depend marginally on the modelled physical processes, while they exhibit a strong dependence on cluster mass. The central and total SZ emission strongly correlates with the cluster X-ray luminosity and temperature. The logarithmic slopes of these scaling relations differ from the self-similar predictions by less than 0.2; the normalization of the relations is lower for simulations including radiative cooling. The observational test suggests that SZ cluster profiles are unlikely to be able to probe the ICM physics. The total SZ decrement appears to be an observable much more robust than the central intensity, and we suggest using the former to investigate scaling relations.     

Visco–Resistive Dissipation in Transient Reconnection Driven by the Orszag–Tang Vortex

Viscous effects are expected to significantly contribute to reconnective energy release mechanisms in solar flares. While simple scaling arguments based on head-on reconnection suggest that viscous dissipation may dominate resistive dissipation, it is not clear whether these findings can be applied in more general merging situations. Here we perform side-by-side planar reconnection simulations driven by the Orszag–Tang vortex, for both classical and Braginskii forms of the viscosity. This formulation has the advantage of providing an autonomous MHD system that develops strong current layers, sustained by large-scale vortical shearing flows. The dissipation rates are shown to follow analytically based scaling laws, which suggest that viscous losses generated from large-scale non-uniform velocity fields are likely to dominate resistive losses in current-sheet reconnection solutions.     

Radiative steady-state colliding stellar wind models: are they correct?

The properties of radiative steady-state colliding stellar winds in binary systems are studied. It is shown that the presence of a singularity at the stagnation point has a major influence on the structure of these flows. This problem is of great importance if their stability properties are considered. None of the existing models treats this mathematical problem properly, and special efforts must be undertaken in the future in order to come to a firm conclusion about the physical nature of possible instabilities. At the moment, neither numerical nor analytical models can be considered to be of acceptable accuracy in the case of highly radiative steady-state colliding stellar winds.