arXiv subjects

Siddhartha Gupta

Publications and source records attributed to Siddhartha Gupta.

At least 19 recordsLinked to original sources

arXiv2025

Impact of Cosmic Ray Distribution on the Growth and Saturation of Bell Instability

Cosmic rays (CRs) streaming in weakly magnetized plasmas can drive large-amplitude magnetic fluctuations via nonresonant streaming instability (NRSI), or Bell instability. Using one-dimensional kinetic simulations, we investigate how mono-energetic and power-law CR momentum distributions influence the growth and saturation of NRSI. The linear growth is governed solely by the CR current and is largely insensitive to the CR distribution. However, the saturation depends strongly on the CR distribution and is achieved through CR isotropization, which quenches the driving current. Mono-energetic CRs effectively amplify the magnetic field and isotropize. For power-law distributions, the lowest-energy CRs dominate current relaxation and magnetic growth, while the highest-energy CRs remain weakly scattered, limiting their contribution to saturation. In the absence of low-energy CRs, high-energy particles amplify magnetic fields effectively and isotropize. Accounting for these effects, we provide a modified saturation prescription valid for both relativistic and nonrelativistic CRs. We propose a layered CR-confinement scenario upstream of astrophysical shocks, relevant to particle acceleration to high energies.

astro-ph.HE↗

arXiv2025

Speed-dependent Threshold for Electron Injection into Diffusive Shock Acceleration

Finding the injection threshold for diffusive shock acceleration (DSA) of electrons in collisionless shocks has been a longstanding unsolved problem. Using first-principles kinetic simulations, we identify the conditions for electron injection into DSA and quantify the evolution of the nonthermal tail in self-generated electromagnetic turbulence. By analyzing electron trajectories and their momentum gain during shock-recrossing cycles, we demonstrate that electrons start participating in DSA when their speed is large enough to overrun the shock. We develop a minimal model showing that speed-dependent injection reproduces nonthermal electron spectra observed in kinetic simulations. Our findings establish a new criterion for electron DSA, which has broad implications for the nonthermal emission of shock-powered space/astrophysical systems.

astro-ph.HE↗

arXiv2024

Nonthermal Signatures of Radiative Supernova Remnants II: The Impact of Cosmic Rays and Magnetic Fields

Near the ends of their lives, supernova remnants (SNRs) enter a "radiative phase," when efficient cooling of the postshock gas slows expansion. Understanding SNR evolution at this stage is crucial for estimating feedback in galaxies, as SNRs are expected to release energy and momentum into the interstellar medium near the ends of their lives. A standard prediction of SNR evolutionary models is that the onset of the radiative stage precipitates the formation of a dense shell behind the forward shock. In Paper I, we showed that such shell formation yields detectable nonthermal radiation from radio to $\gamma$-rays, most notably emission brightening by nearly two orders of magnitude. However, there remains no observational evidence for such brightening, suggesting that this standard prediction needs to be investigated. In this paper, we perform magneto-hydrodynamic simulations of SNR evolution through the radiative stage, including cosmic rays (CRs) and magnetic fields to assess their dynamical roles. We find that both sources of nonthermal pressure disrupt shell formation, reducing shell densities by a factor of a few to more than an order of magnitude. We also use a self-consistent model of particle acceleration to estimate the nonthermal emission from these modified SNRs and demonstrate that, for reasonable CR acceleration efficiencies and magnetic field strengths, the nonthermal signatures of shell formation can all but disappear. We therefore conclude that the absence of observational signatures of shell formation represents strong evidence that nonthermal pressures from CRs and magnetic fields play a critical dynamical role in late-stage SNR evolution.

astro-ph.HE↗

arXiv2024

Understanding Streaming Instabilities in the Limit of High Cosmic Ray Current Density

A critical component of particle acceleration in astrophysical shocks is the non-resonant (Bell) instability, where the streaming of cosmic rays (CRs) leads to the amplification of magnetic fields necessary to scatter particles. In this work we use kinetic particle-in-cells simulations to investigate the high-CR current regime, where the typical assumptions underlying the Bell instability break down. Despite being more strongly driven, significantly less magnetic field amplification is observed compared to low-current cases, an effect due to the anisotropic heating that occurs in this regime. We also find that electron-scale modes, despite being fastest growing, mostly lead to moderate electron heating and do not affect the late evolution or saturation of the instability.

astro-ph.HE↗

arXiv2024

Electron Acceleration at Quasi-parallel Non-relativistic Shocks: A 1D Kinetic Survey

We present a survey of 1D kinetic particle-in-cell simulations of quasi-parallel non-relativistic shocks to identify the environments favorable for electron acceleration. We explore an unprecedented range of shock speeds $v_{\rm sh}\approx 0.067-0.267\,c$, Alfv\'{e}n Mach numbers $\mathcal{M}_{\rm A} = 5-40$, sonic Mach numbers $\mathcal{M}_{\rm s} = 5-160$, as well as the proton-to-electron mass ratios $m_{\rm i}/m_{\rm e}=16-1836$. We find that high Alfv\'{e}n Mach number shocks can channel a large fraction of their kinetic energy into nonthermal particles, self-sustaining magnetic turbulence and acceleration to larger and larger energies. The fraction of injected particles is $\lesssim 0.5\%$ for electrons and $\approx 1\%$ for protons, and the corresponding energy efficiencies are $\lesssim 2\%$ and $\approx 10\%$, respectively. The extent of the nonthermal tail is sensitive to the Alfv\'{e}n Mach number; when $\mathcal{M}_{\rm A}\lesssim 10$, the nonthermal electron distribution exhibits minimal growth beyond the average momentum of the downstream thermal protons, independently of the proton-to-electron mass ratio. Acceleration is slow for shocks with low sonic Mach numbers, yet nonthermal electrons still achieve momenta exceeding the downstream thermal proton momentum when the shock Alfv\'{e}n Mach number is large enough. We provide simulation-based parametrizations of the transition from thermal to nonthermal distribution in the downstream (found at a momentum around $p_{\rm i,e}/m_{\rm i}v_{\rm sh} \approx 3\sqrt{m_{\rm i,e}/m_{\rm i}}$), as well as the ratio of nonthermal electron to proton number density. The results are applicable to many different environments and are important for modeling shock-powered nonthermal radiation.

astro-ph.HE↗

arXiv2024

Modeling the Saturation of the Bell Instability using Hybrid Simulations

The nonresonant streaming instability (Bell instability) plays a pivotal role in the acceleration and confinement of cosmic rays (CRs); yet, the exact mechanism responsible for its saturation and the magnitude of the final amplified magnetic field have not been assessed from first-principles. Using a survey of hybrid simulations (with kinetic ions and fluid electrons), we study the evolution of the Bell instability as a function of the parameters of the CR population. We find that, at saturation, the magnetic pressure in the amplified field is comparable with the initial CR anisotropic pressure, rather than with the CR energy flux as previously argued. These results provide a predictive prescription for the total magnetic field amplification expected in the many astrophysical environments where the Bell instability is important.

astro-ph.HE↗

arXiv2023

Return Currents in Collisionless Shocks

Collisionless shocks tend to send charged particles into the upstream, driving electric currents through the plasma. Using kinetic particle-in-cell simulations, we investigate how the background thermal plasma neutralizes such currents in the upstream of quasi-parallel non-relativistic electron-proton shocks. We observe distinct processes in different regions: the far upstream, the shock precursor, and the shock foot. In the far upstream, the current is carried by nonthermal protons, which drive electrostatic modes and produce supra-thermal electrons that move towards upstream infinity. Closer to the shock (in the precursor), both the current density and the momentum flux of the beam increase, which leads to electromagnetic streaming instabilities that contribute to the thermalization of supra-thermal electrons. At the shock foot, these electrons are exposed to shock-reflected protons, resulting in a two-stream type instability. We analyze these processes and the resulting heating through particle tracking and controlled simulations. In particular, we show that the instability at the shock foot can make the effective thermal speed of electrons comparable to the drift speed of the reflected protons. These findings are important for understanding both the magnetic field amplification and the processes that may lead to the injection of supra-thermal electrons into diffusive shock acceleration.

astro-ph.HE↗

arXiv2023

Evidence for multiple shocks from the $γ$-ray emission of RS Ophiuchi

In August of 2021, Fermi-LAT, H.E.S.S., and MAGIC detected GeV and TeV $γ$-ray emission from an outburst of recurrent nova RS Ophiuchi. This detection represents the first very high energy $γ$-rays observed from a nova, and opens a new window to study particle acceleration. Both H.E.S.S. and MAGIC described the observed $γ$-rays as arising from a single, external shock. In this paper, we perform detailed, multi-zone modeling of RS Ophiuchi's 2021 outburst including a self-consistent prescription for particle acceleration and magnetic field amplification. We demonstrate that, contrary to previous work, a single shock cannot simultaneously explain RS Ophiuchi's GeV and TeV emission, particularly the spectral shape and distinct light curve peaks. Instead, we put forward a model involving multiple shocks that reproduces the observed $γ$-ray spectrum and temporal evolution. The simultaneous appearance of multiple distinct velocity components in the nova optical spectrum over the first several days of the outburst supports the presence of distinct shocks, which may arise either from the strong latitudinal dependence of the density of the external circumbinary medium (e.g., in the binary equatorial plane versus the poles) or due to internal collisions within the white dwarf ejecta (as powers the $γ$-ray emission in classical novae).

astro-ph.HE↗

arXiv2022

A Kinetic Study of the Saturation of the Bell Instability

The nonresonant cosmic ray instability, predicted by Bell (2004), is thought to play an important role in the acceleration and confinement of cosmic rays (CR) close to supernova remnants. Despite its importance, the exact mechanism responsible for the saturation of the instability has not been determined, and there is no first-principle prediction for the amplitude of the saturated magnetic field. Using a survey of self-consistent hybrid simulations (with kinetic ions and fluid electrons), we study the non-linear evolution of the Bell instability as a function of the parameters of the CR population. We find that saturation is achieved when the magnetic pressure in the amplified field is comparable to the initial CR momentum flux.

astro-ph.HE↗

arXiv2022

Cosmic rays from massive star clusters : A close look at Westerlund 1

We study the effect of cosmic ray (CR) acceleration in the massive compact star cluster Westerlund 1 in light of its recent detection in $γ$-rays. Recent observations reveal a $1/r$ radial distribution of the CR energy density. Here we theoretically investigate whether or not this profile can help to distinguish between (1) continuous CR acceleration in the star cluster stellar wind-driven shocks and (2) discrete CR acceleration in multiple supernovae shocks -- which are often debated in the literature. Using idealized two-fluid simulations and exploring different acceleration sites and diffusion coefficients, we obtain the CR energy density profile and luminosity to find the best match for the $γ$-ray observations. We find that the inferred CR energy density profiles from observations of $γ$-ray luminosity and mass can be much different from the true radial profile. CR acceleration at either the cluster core region or the wind termination shock can explain the observations, if the diffusion coefficient is $κ_{\rm cr}\sim 10^{27}$ cm$^2$ s$^{-1}$ and a fraction of $\approx 10\%-20\%$ of the shock power/post-shock pressure is deposited into the CR component. We also study the possibility of discrete supernovae (SN) explosions being responsible for CR acceleration and find that with an injection rate of 1 SN in every $\sim 0.03$ Myr, one can explain the observed $γ$-ray profile. This multiple SN scenario is consistent with X-ray observations only if the thermal conductivity is close to the Spitzer value.

astro-ph.HE↗

arXiv2021

Non-resonant Streaming Instability driven by Leptons

Using fully-kinetic plasma simulations, we study the non-resonant (Bell) streaming instability driven by energetic leptons. We identify the necessary conditions to drive it and the differences from the standard proton-driven case in both linear and saturated stages. A simple analytic theory is presented to explain simulations. Our findings are crucial for understanding the phenomenology of astrophysical environments where only electrons may be accelerated (e.g., oblique shocks) or where relativistic pairs are produced (e.g., around pulsar wind nebulae).

astro-ph.HE↗

arXiv2021

Lepton-driven Non-resonant Streaming Instability

A strong super-Alfvénic drift of energetic particles (or cosmic rays, CRs) in a magnetized plasma can amplify the magnetic field significantly through non-resonant streaming instability (NRSI). While the traditional analysis is done for an ion current, here we use kinetic particle-in-cell simulations to study how the NRSI behaves when it is driven by electrons or by a mixture of electrons and positrons. In particular, we characterize growth rate, spectrum, and helicity of the unstable modes, as well the level of magnetic field at saturation. Our results are potentially relevant for several space/astrophysical environments (e.g, electron strahl in the solar wind, at oblique non-relativistic shocks, around pulsar wind nebulae) and also in laboratory experiments.

astro-ph.HE↗

arXiv2021

A numerical approach to the non-uniqueness problem of cosmic ray two-fluid equations at shocks

Cosmic rays (CRs) are frequently modeled as an additional fluid in hydrodynamic (HD) and magnetohydrodynamic (MHD) simulations of astrophysical flows. The standard CR two-fluid model is described in terms of three conservation laws (expressing conservation of mass, momentum and total energy) and one additional equation (for the CR pressure) that cannot be cast in a satisfactory conservative form. The presence of non-conservative terms with spatial derivatives in the model equations prevents a unique weak solution behind a shock. We investigate a number of methods for the numerical solution of the two-fluid equations and find that, in the presence of shock waves, the results generally depend on the numerical details (spatial reconstruction, time stepping, the CFL number, and the adopted discretization). All methods converge to a unique result if the energy partition between the thermal and non-thermal fluids at the shock is prescribed using a subgrid prescription. This highlights the non-uniqueness problem of the two-fluid equations at shocks. From our numerical investigations, we report a robust method for which the solutions are insensitive to the numerical details even in absence of a subgrid prescription, although we recommend a subgrid closure at shocks using results from kinetic theory. The subgrid closure is crucial for a reliable post-shock solution and also its impact on large scale flows because the shock microphysics that determines CR acceleration is not accurately captured in a fluid approximation. Critical test problems, limitations of fluid modeling, and future directions are discussed.

astro-ph.HE↗

arXiv2020

Role of cosmic rays in the early stages of galactic outflows

Using an idealized set-up, we investigate the dynamical role of cosmic rays (CRs) in the early stages of galactic outflows for galaxies of halo masses $10^{8}$, $10^{11}$ and $10^{12}$ $M_\odot$. The outflow is launched from a central region in the galactic disk where we consider three different constant star formation rates ($0.1$, $1$, and $10$ $M_{\odot}$ yr$^{-1}$) over a dynamical timescale of $50$ Myr. We determine the temperature distribution of the gas and find that CRs can reduce the temperature of the shocked gas, which is consistent with previous results. However, we show that CRs do not have any noticeable effect on the mass loading by the outflow. We find that CRs can reduce the size of the outflow, which contradicts previous claims of efficient dynamical impact of CRs; however, it is consistent with earlier theoretical models of cosmic ray driven blastwave as well as stellar wind. We discuss the dependence of our results on CR injection prescriptions and compare them with earlier studies. We conclude that in the early stages of galactic outflows the dynamical role of CRs is not important.

astro-ph.GA↗

arXiv2019

Realistic modeling of wind and supernovae shocks in star clusters: addressing ${\rm ^{22}Ne/^{20}Ne}$ and other problems in Galactic cosmic rays

Cosmic ray (CR) sources leave signatures in the isotopic abundances of CRs. Current models of Galactic CRs that consider supernovae (SNe) shocks as the main sites of particle acceleration cannot satisfactorily explain the higher ${\rm ^{22}Ne/^{20}Ne}$ ratio in CRs compared to the interstellar medium. Although stellar winds from massive stars have been invoked, their contribution relative to SNe ejecta has been taken as a free parameter. Here we present a theoretical calculation of the relative contributions of wind termination shocks (WTSs) and SNe shocks in superbubbles, based on the hydrodynamics of winds in clusters, the standard stellar mass function, and stellar evolution theory. We find that the contribution of WTSs towards the total CR production is at least $25\%$, which rises to $\gtrsim 50\%$ for young ($\lesssim 10$ Myr) clusters, and explains the observed $^{22}{\rm Ne}/^{20} {\rm Ne}$ ratio. We argue that since the progenitors of apparently isolated supernovae remnants (SNRs) are born in massive star clusters, both WTS and SNe shocks can be integrated into a combined scenario of CRs being accelerated in massive clusters. This scenario is consistent with the observed ratio of SNRs to $γ$-ray bright ($L_γ\gtrsim 10^{35}$ erg s$^{-1}$) star clusters, as predicted by star cluster mass function. Moreover, WTSs can accelerate CRs to PeV energies, and solve other longstanding problems of the standard supernova paradigm of CR acceleration.

astro-ph.HE↗

arXiv2019

Holographic shear rheology of viscoelastic fluids

In this study, we report the use of digital holography microscopy (DHM) for 3D-resolved flow kinematics and shear rheometry of viscoelastic polymeric fluids. We computationally reconstruct the recorded holograms to visualize the tracer imbued flow volume in microchannels, followed by implementation of particle tracking velocimetry (PTV) to quantitate spatially-resolved velocity fields in 3D. In order to select optimal parameters for DHM-PTV characterization of complex fluids, we studied the effect of hologram recording distance, seeding density and particle size. Using the optimal parameters, we show quantitative characterization of the shear rheology from the velocity fields without any a-priori assumptions of wall boundary condition or constitutive equation. The viscosity versus shear rate data for Newtonian and polyethylene oxide solutions could be measured in the range of ~ 0.05 - 20,000 s-1 with just four input flow rates. This data from holographic shear rheometry was found to be in good agreement with computational fluid dynamics simulations and macrorheometry. The holographic shear rheology technique remained unaffected by wall-slip events and instead provided an avenue to quantitate slip severity. Finally, we discuss holographic visualization of particle migration in microfluidic flows which can limit flow field access while at the same time provide a fingerprint of the suspending fluid rheology.

physics.flu-dyn↗

arXiv2018

Constraining cosmic ray acceleration in young star clusters using multi-wavelength observations

We use $1$D and $3$D two-fluid cosmic ray (CR) hydrodynamic simulations to investigate the role of CRs in the vicinity of a compact young star cluster. We model a self-gravitating cloud (density profile $ρ\propto r^{-1}$), include important thermal and non-thermal processes, and explore two different CR injection scenarios. We show that if internal shocks in the wind-driving region are the main site for CR acceleration, then the resulting $γ$-ray luminosity ($L_{\rm γ}$) can reach $\approx 5\%$ of the mechanical luminosity ($L_{\rm w}$), independent of the fraction of wind energy ($\sim 1-20\%$) injected into CRs. In contrast, if the forward/reverse shock of a bubble is the injection site then $L_{\rm γ}$ increases linearly with the CR injection fraction, as expected analytically. We find that the X-ray luminosity ($L_{\rm x}$) in the forward/reverse shock injection scenario is $\gtrsim 10^{-3} L_{\rm w}$, which is $\sim 10$ times larger than in the central wind-driving injection case. We predict the corresponding range of the synchrotron radio luminosity. We show how multi-wavelength observations can constrain the CR parameters. Comparing the predicted multi-wavelength luminosities with those of 30 Doradus we identify the reverse shock as the most probable CR injection site, and that thermal conduction is important. We do not find significant dynamical impact of CRs in our models.

astro-ph.GA↗

arXiv2017

Lack of thermal energy in superbubbles: hint of cosmic rays?

Using analytic methods and $1$-D two-fluid simulations, we study the effect of cosmic rays (CRs) on the dynamics of interstellar superbubbles (ISBs) driven by multiple supernovae (SNe)/stellar winds in OB associations. In addition to CR advection and diffusion, our models include thermal conduction and radiative cooling. We find that CR injection at the reverse shock or within a central wind-driving region can affect the thermal profiles of ISBs and hence their X-ray properties. Even if a small fraction ($10-20\%$) of the total mechanical power is injected into CRs, a significant fraction of the ram pressure at the reverse shock can be transferred to CRs. The energy transfer becomes efficient if (1) the reverse shock gas Mach number exceeds a critical value ($M_{\rm th}\gtrsim 12$) and (2) the CR acceleration time scale $τ_{\rm acc}\sim κ_{\rm cr}/v^2$ is shorter than the dynamical time, where $κ_{\rm cr}$ is CR diffusion constant and $v$ is the upstream velocity. We show that CR affected bubbles can exhibit a volume averaged hot gas temperature $1-5\times10^{6}$ K, lower by a factor of $2-10$ than without CRs. Thus CRs can potentially solve the long-standing problem of the observed low ISB temperatures.

astro-ph.GA↗