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Research Interests

  • Computational Fluid Dynamics : Hydrodynamics, Magneto-hydrodynamics & Radiative transfer
  • Particle Acceleration in AGN jets : Modeling Non-Thermal spectral signature
  • Space Weather and Space Plasma Modelling
  • Accretion disk physics, Jets and Outflow formation.
  • Astrophysical Code Development : MPI Parallel Programming, Visualization software tools, best practices of coding with C and Python.
  • Inter-Stellar Medium : Shock-Cloud Interaction, Collapse of molecular cores, Shock induced chemistry.

List of Recent Selected Published Works

For latest simulation movies and talks presented by members from our group on on-going work,
please refer to our Youtube Channel

Effects of a Velocity Shear on Double Current Sheet Systems: Explosive Reconnection and Particle Acceleration

(Top) Trajectory of highest energy particle that is being accelerated due to first order Fermi process within the plasmoid formed due to reconnection (Bottom) Temporal evolution of in plane (IP) and out of plane (OP) components of energy for the particle.

The effect of a parallel velocity shear on the explosive phase of a double current sheet system is investigated within the 2D resistive magnetohydrodynamic (MHD) framework. We further explore the effect of this shear on acceleration of test particles. The general evolution pattern of the double current sheets is similar for all sub-Alfv\'enic shears with respect to the initial transient phase, the onset of the plasmoid instability and the final relaxation phase. We find that the theoretical scaling of the reconnection rate with shear holds if the rate is measured when the islands have a similar size. The larger island widths for lower shears greatly enhance the reconnection rate during the explosive phase. We have further examined the modification of the energy spectrum of the accelerated particles in the presence of a shear. Our results also show that the flow only modifies the high energy tail of the particle spectrum and has negligible effect on the power-law index. Individual particle trajectories help to explore the various mechanisms associated with the acceleration. Based on the location of the particles, the acceleration mechanisms are found to vary. We highlight the importance of the convective electric field in the inflow as well as the outflow region inside large magnetic islands in the acceleration of particles. The interaction and reflection of the particles with the reconnection exhausts inside the large scale primary magnetic islands is found to have a significant effect on the energization of the particles. The videos of time evolution of current density J for two different shears are shown below (Left) : shear speed Vs = 0.0 Va, (Right) with shear speed Vs = 0.75 Va

Numerical analysis of long-term variability of AGN jets through RMHD simulations

(Left) Density distribution from 3D Relativistic MHD simulations showing kink instability along with tangled magnetic field lines. (Right) Synthetic light curve (for ~ 20 years) generated from kink unstable jet and viewed from two different viewing angles showing long term variablity due to helical jet model.

Relativistic AGN (active galactic nucleus) jets exhibit multitime-scale variability and a broad-band non-thermal spectrum extending from radio to gamma-rays. These highly magnetized jets are prone to undergo several magnetohydrodynamic (MHD) instabilities during their propagation in space and could trigger jet radiation and particle acceleration. This work aims to study the implications of relativistic kink mode instability on the observed long-term variability in the context of the twisting in-homogeneous jet model. To achieve this, we investigate the physical configurations preferable for forming kink mode instability by performing high-resolution 3D relativistic MHD simulations of a portion of highly magnetized jets. In particular, we perform simulations of cylindrical plasma column with Lorentz factor ≥5 and study the effects of magnetization values and axial wavenumbers with decreasing pitch on the onset and growth of kink instability. We have confirmed the impact of axial wavenumber on the dynamics of the plasma column including the growth of the instability. In this work, we have further investigated the connection between the dynamics of the plasma column with its time-varying emission features. From our analysis, we find a correlated trend between the growth rate of kink mode instability and the flux variability obtained from the simulated light curve.

Jets, disc-winds and oscillations in general relativistic, magnetically driven flows around black hole

Cartoon figure showing the different jet and wind regions
from our simulations of MAD disc.

Relativistic jets and disc-winds are typically observed in BH-XRBs and AGNs. However, many physical details of jet launching and the driving of disc winds from the underlying accretion disc are still not fully understood. In this study, we further investigate the role of the magnetic field strength and structure in launching jets and disc winds. In particular, we explore the connection between jet, wind, and the accretion disc around the central black hole. We perform axisymmetric GRMHD simulations of the accretion-ejection system using adaptive mesh refinement. Essentially, our simulations are initiated with a thin accretion disc in equilibrium. An extensive parametric study by choosing different combinations of magnetic field strength and initial magnetic field inclination is also performed. Our study finds relativistic jets driven by the Blandford \& Znajek (BZ) mechanism and the disc-wind driven by the Blandford \& Payne (BP) mechanism. We also find that plasmoids are formed due to the reconnection events, and these plasmoids advect with disc-winds. As a result, the tension force due to the poloidal magnetic field is enhanced in the inner part of the accretion disc, resulting in disc truncation and oscillation. These oscillations result in flaring activities in the jet mass flow rates. We find simulation runs with a lower value of the plasma-$\beta$, and lower inclination angle parameters are more prone to the formation of plasmoids and subsequent inner disc oscillations. Our models provide a possible template to understand spectral state transition phenomena in BH-XRBs.

Numerical study of Kelvin-Helmholtz instability and its impact on synthetic emission from magnetized jets

(Top) Production of secondary electron population due to shocks seen in background color image pf density.
(Bottom) The evolution of synthetic SEDs showing synchrotron (left) and IC (right).

Non-thermal emission from Active Galactic Nuclei (AGN) jets extends up-to large scales in-spite of them being prone to a slew of magneto-hydrodynamic instabilities. The main focus of this study is to understand the impact of MHD instabilities on the non-thermal emission from large-scale AGN jets. We perform high-resolution three-dimensional numerical magneto-hydrodynamic simulations of a plasma column to investigate the dynamical and emission properties of jet configurations at kilo-parsec scales with different magnetic field profiles, jet speeds, and density contrast. We also obtain synthetic non-thermal emission signatures for different viewing angles using an approach that assumes static particle spectra and that obtained by evolving the particle spectra using Lagrangian macro-particles incorporating the effects of shock acceleration and radiative losses. We find that the shocks due to Kelvin-Helmholtz (KH) instability in the axial magnetic field configurations can strongly affect the jet dynamics. Additionally, we also find the presence of weak biconical shocks in the under-dense jet columns. The inclusion of a helical magnetic field hinders the vortex growth at the shear surface thereby stabilizing the jet column. With the evolving particle spectra approach, the synthetic SEDs obtained for cases with strong KH instability show the presence of multiple humps ranging from radio to TeV gamma-ray band. We conclude that the high-energy electrons accelerated in the vicinity of freshly formed shocks due to KH instability, result in high X-ray emission.

Simulating the dynamics and synchrotron emission from relativistic jets II. Evolution of non-thermal electrons

Distribution of particles coloured with their lorentz factor in a jet cocoon.

We have simulated the evolution of non-thermal cosmic ray electrons (CREs) in 3D relativistic magneto hydrodynamic (MHD) jets evolved up to a height of 9 kpc. The CREs have been evolved in space and in energy concurrently with the relativistic jet fluid, duly accounting for radiative losses and acceleration at shocks. We show that jets stable to MHD instabilities show expected trends of regular flow of CREs in the jet spine and acceleration at a hotspot followed by a settling backflow. However, unstable jets create complex shock structures at the jet-head (kink instability), the jet spine-cocoon interface and the cocoon itself (Kelvin-Helmholtz modes). CREs after exiting jet-head undergo further shock crossings in such scenarios and are re-accelerated in the cocoon. CREs with different trajectories in turbulent cocoons have different evolutionary history with different spectral parameters. Thus at the same spatial location, there is mixing of different CRE populations, resulting in a complex total CRE spectrum when averaged over a given area. Cocoons of unstable jets can have an excess build up of energetic electrons due to re-acceleration at turbulence driven shocks and slowed expansion of the decelerated jet. This will add to the non-thermal energy budget of the cocoon.

A comparison study of extrapolation models and empirical relations in forecasting solar wind

Results obtained from physics based solar wind model
and its comparison with observed data.

Coronal mass ejections (CMEs) and high speed solar streams serve as perturbations to the background solar wind that have major implications in space weather dynamics. Therefore, a robust framework for accurate predictions of the background wind properties is a fundamental step towards the development of any space weather prediction toolbox. In this pilot study, we focus on the implementation and comparison of various models that are critical for a steady state, solar wind forecasting framework. Specifically, we perform case studies on Carrington rotations 2053, 2082 and 2104, and compare the performance of magnetic field extrapolation models in conjunction with velocity empirical formulations to predict solar wind properties at Lagrangian point L1. Two different models to extrapolate the solar wind from the coronal domain to the inner-heliospheric domain are presented, namely, (a) Kinematics based (Heliospheric Upwind eXtrapolation [HUX]) model and (b) Physics based model. The physics based model solves a set of conservative equations of hydrodynamics using the PLUTO code and can additionally predict the thermal properties of solar wind. The assessment in predicting solar wind parameters of the different models is quantified through statistical measures. We further extend this developed framework to also assess the polarity of inter-planetary magnetic field at L1. Our best models for the case of CR2053 gives a very high correlation coefficient ( ∼ 0.73-0.81) and has an root mean square error of ( ∼ 75-90 kms −1 ). Additionally, the physics based model has a standard deviation comparable with that obtained from the hourly OMNI solar wind data and also produces a considerable match with observed solar wind proton temperatures measured at L1 from the same database.

A Particle Module for the PLUTO Code. III. Dust

Result for Vertical oscillation test of dust particles
along with convergence study with different Stokes numbers

Implementation of a new particle module describing the physics of dust grains coupled to a gas via drag forces is the subject of this work. The proposed particle-gas hybrid scheme has been designed to work in Cartesian as well as in cylindrical and spherical geometries. The numerical method relies on a Godunov-type second-order scheme for the fluid and an exponential midpoint rule for dust particles, which overcomes the stiffness introduced by the linear coupling term. Besides being time-reversible and globally second-order accurate in time, the exponential integrator provides energy errors that are always bounded, and it remains stable in the limit of arbitrarily small particle stopping times, yielding the correct asymptotic solution. Such properties make this method preferable to the more widely used semi-implicit or fully implicit schemes at a very modest increase in computational cost. Coupling between particles and grid quantities is achieved through particle deposition and field-weighting techniques borrowed from particle-in-cell simulation methods. In this respect, we derive new weight factors in curvilinear coordinates that are more accurate than traditional volume or area weighting. A comprehensive suite of numerical benchmarks is presented to assess the accuracy and robustness of the algorithm in Cartesian, cylindrical, and spherical coordinates. Particular attention is devoted to the streaming instability, which is analyzed in both local and global disk models. The module is part of the PLUTO code for astrophysical gas dynamics, and it is mainly intended for the numerical modeling of protoplanetary disks in which solid and gas interact via aerodynamic drag.

Modeling Star-Planet Interactions in Far-out Planetary and Exoplanetary Systems

3D steady-state magnetospheric configurations
with no tilt and extreme tilt angles for both S-IMF and N-IMF cases.

The magnetized wind from a host star plays a vital role in shaping the magnetospheric configuration of the planets it harbors. We carry out three-dimensional (3D) compressible magnetohydrodynamic simulations of the interactions between magnetized stellar winds and planetary magnetospheres corresponding to a far-out star-planet system, with and without planetary dipole obliquity. We identify the pathways that lead to the formation of a dynamical steady-state magnetosphere and find that magnetic reconnection plays a fundamental role in the process. The magnetic energy density is found to be greater on the nightside than on the dayside, and the magnetotail is comparatively more dynamic. It is found that stellar wind plasma injection into the inner magnetosphere is possible through the magnetotail. We further study magnetospheres with extreme tilt angles, keeping in perspective the examples of Uranus and Neptune. High dipole obliquities may also manifest due to polarity excursions during planetary field reversals. We find that global magnetospheric reconnection sites change for large planetary dipole obliquity, and more complex current sheet structures are generated. We discuss the implications of these findings for atmospheric erosion, the introduction of stellar and interplanetary species that modify the composition of the atmosphere, auroral activity, and magnetospheric radio emission. This study is relevant for exploring star-planet interactions and its consequence on atmospheric dynamics and habitability in solar system planets and exoplanets.

A Particle Module for the PLUTO Code II - Hybrid Framework for Modeling Non-thermal emission from Relativistic Magnetized flows

Cartoon figure showing the hybrid framework of
incorporating Lagrangian particles on fixed Eulerian grid.

We describe a new hybrid framework to model non-thermal spectral signatures from highly energetic particles embedded in a large-scale classical or relativistic MHD flow. Our method makes use of Lagrangian particles moving through an Eulerian grid where the (relativistic) MHD equations are solved concurrently. Lagrangian particles follow fluid streamlines and represent ensembles of (real) relativistic particles with a finite energy distribution. The spectral distribution of each particle is updated in time by solving the relativistic cosmic ray transport equation based on local fluid conditions. This enables us to account for a number of physical processes, such as adiabatic expansion, synchrotron and inverse Compton emission. An accurate semi-analytically numerical scheme that combines the method of characteristics with a Lagrangian discretization in the energy coordinate is described.In presence of (relativistic) magnetized shocks, a novel approach to consistently model particle energization due to diffusive shock acceleration has been presented.

Multi-wavelength emission and polarisation maps of oblique shocks in slab jets.

Our approach relies on a refined shock-detection algorithm and updates the particle energy distribution based on the shock compression ratio, magnetic field orientation and amount of (parameterized) turbulence.The evolved distribution from each Lagrangian particle is further used to produce observational signatures like emission maps and polarization signals accounting for proper relativistic corrections. We further demonstrate the validity of this hybrid framework using standard numerical benchmarks and evaluate the applicability of such a tool to study high energy emission from extra-galactic jets.

A Particle Module for the PLUTO Code. I. An Implementation of the MHD–PIC Equations

Density snapshots for the collisionless shock problem at four different times. Only a reduced portion of the domain, in proximity of the unperturbed shock position is shown.

We describe an implementation of a particle physics module available for the PLUTO code appropriate for the dynamical evolution of a plasma consisting of a thermal fluid and a nonthermal component represented by relativistic charged particles or cosmic rays (CRs). While the fluid is approached using standard numerical schemes for magnetohydrodynamics, CR particles are treated kinetically using conventional Particle-In-Cell (PIC) techniques. The module can be used either to describe test-particle motion in the fluid electromagnetic field or to solve the fully coupled magnetohydrodynamics (MHD)–PIC system of equations with particle backreaction on the fluid as originally introduced by Bai et al. Particle backreaction on the fluid is included in the form of momentum–energy feedback and by introducing the CR-induced Hall term in Ohm’s law. The hybrid MHD–PIC module can be employed to study CR kinetic effects on scales larger than the (ion) skin depth provided that the Larmor gyration scale is properly resolved. When applicable, this formulation avoids resolving microscopic scales, offering substantial computational savings with respect to PIC simulations.We present a fully conservative formulation that is second-order accurate in time and space, and extends to either the Runge–Kutta (RK) or the corner transport upwind time-stepping schemes (for the fluid), while a standard Boris integrator is employed for the particles. For highly energetic relativistic CRs and in order to overcome the time-step restriction, a novel subcycling strategy that retains second-order accuracy in time is presented. Numerical benchmarks and applications including Bell instability, diffusive shock acceleration, and test-particle acceleration in reconnecting layers are discussed.

Simulation of MHD modes in Active Region of Sun.

There is considerable observational evidence of implosion of magnetic loop systems inside solar coronal active regions following high-energy events like solar flares. In this work, we propose that such collapse can be modeled in three dimensions quite accurately within the framework of ideal magnetohydrodynamics. We furthermore argue that the dynamics of loop implosion is only sensitive to the transmitted disturbance of one or more of the system variables, e.g., velocity generated at the event site. This indicates that to understand loop implosion, it is sensible to leave the event site out of the simulated active region. Toward our goal, a velocity pulse is introduced to model the transmitted disturbance generated at the event site. Magnetic field lines inside our simulated active region are traced in real time, and it is demonstrated that the subsequent dynamics of the simulated loops closely resemble observed imploding loops. Our work highlights the role of plasma β in regards to the rigidity of the loop systems and how that might affect the imploding loops’ dynamics. Compressible magnetohydrodynamic modes such as kink and sausage are also shown to be generated during such processes, in accordance with observations.

Density evolution along a field line showing indicatication of the standing sausage wave oscillation.

Runge-Kutta Legendre Method for Parabolic PDEs in PLUTO code : Application to Thermal Conduction Problems.

Effect of Anisotropic Thermal conduction in the problem of 2D blast wave.

An important ingredient in numerical modelling of high temperature magnetized astrophysical plasmas is the anisotropic transport of heat along magnetic field lines from higher to lower temperatures. Magnetohydrodynamics typically involves solving the hyperbolic set of conservation equations along with the induction equation. Incorporating anisotropic thermal conduction requires to also treat parabolic terms arising from the diffusion operator. An explicit treatment of parabolic terms will considerably reduce the simulation time step due to its dependence on the square of the grid resolution ( x) for stability. Although an implicit scheme relaxes the constraint on stability, it is difficult to distribute efficiently on a parallel architecture.

Strong scaling test for the newly implemented Runge-Kutta Legendre Method in PLUTO code.

Treating parabolic terms with accelerated super-time- stepping (STS) methods has been discussed in literature, but these methods suffer from poor accuracy (first order in time) and also have difficult-to- choose tuneable stability parameters. In this work, we highlight a second-order (in time) Runge–Kutta–Legendre (RKL) scheme (first described by Meyer, Balsara & Aslam 2012) that is robust, fast and accurate in treating parabolic terms alongside the hyperbolic conversation laws. We demonstrate its superiority over the first-order STS schemes with standard tests and astrophysical applications. We also show that explicit conduction is particularly robust in handling saturated thermal conduction. Parallel scaling of explicit conduction using RKL scheme is demonstrated up to more than 104 processors.

Interaction of Hydrodynamic Shock with Self-gravitating cloud.

Time evolution of density (X-Y plane) of interaction of 3D self-gravitating cloud with weak shock

We describe the results of 3D simulations of the interaction of hydrodynamic shocks with Bonnor-Ebert spheres performed with an adaptive mesh refinement code. The calculations are isothermal and the clouds are embedded in a medium in which the sound speed is either 4 or 10 times that in the cloud. The strengths of the shocks are such that they induce gravitational collapse in some cases and not in others, and we derive a simple estimate for the shock strength required for this to occur. These results are relevant to dense cores and Bok globules in star-forming regions subjected to shocks produced by stellar feedback.

Interplay Magnetic reconnection and non-axisymmetric instabilities in Jets.

Formation of short wavelength pressure driven instabilities in density of jet column with toroidal magnetic field lines.

Magnetic reconnection is a plasma phenomenon where a topological rearrangement of magnetic field lines with opposite polarity results in dissipation of magnetic energy into heat, kinetic energy and particle acceleration. Such a phenomenon is considered as an efficient mechanism for energy release in laboratory and astrophysical plasmas. An important question is how to make the process fast enough to account for observed explosive energy releases. The classical model for steady state magnetic reconnection predicts reconnection times scaling as S 1/2 (where S is the Lundquist number) and yields time-scales several order of magnitude larger than the observed ones. Earlier two- dimensional MHD simulations showed that for large Lundquist number the reconnection time becomes independent of S (`fast reconnection' regime) due to the presence of the secondary tearing instability that takes place for S ≳ 1 × 10 4 . We report on our 3D MHD simulations of magnetic reconnection in a magnetically confined cylindrical plasma column under either a pressure balanced or a force-free equilibrium and compare the results with 2D simulations of a circular current sheet. We find that the 3D instabilities acting on these configurations result in a fragmentation of the initial current sheet in small filaments, leading to enhanced dissipation rate that becomes independent of the Lundquist number already at S ≃ 1 × 10 3 .

The dominant kink mode for current driven instability seen in the density along turbulent current sheets.