# Anatoly Spitkovsky - Princeton

## Contact Details

NameAnatoly Spitkovsky |
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AffiliationPrinceton |
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CityPrinceton |
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CountryUnited States |
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## Pubs By Year |
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## Pub CategoriesHigh Energy Astrophysical Phenomena (39) Astrophysics (11) Physics - Plasma Physics (9) Astrophysics of Galaxies (3) Physics - Space Physics (2) Cosmology and Nongalactic Astrophysics (2) High Energy Physics - Theory (1) Solar and Stellar Astrophysics (1) Physics - Geophysics (1) Instrumentation and Methods for Astrophysics (1) |

## Publications Authored By Anatoly Spitkovsky

**Affiliations:**

^{1}University of Chicago,

^{2}Princeton University,

^{3}Princeton University

We study the thermalization, injection, and acceleration of ions with different mass/charge ratios, $A/Z$, in non-relativistic collisionless shocks via hybrid (kinetic ions-fluid electrons) simulations. In general, ions thermalize to a post-shock temperature proportional to $A$. When diffusive shock acceleration is efficient, ions develop a non-thermal tail whose extent scales with $Z$ and whose normalization is enhanced as $(A/Z)^2$, so that incompletely-ionized heavy ions are preferentially accelerated. Read More

Accreting pulsars power relativistic jets, and display a complex spin phenomenology. These behaviours may be closely related to the large-scale configuration of the star's magnetic field. The total torque experienced by the pulsar comprises spin-up and spin-down contributions from different bundles of magnetic field lines; the spin-down `braking' torque is applied both by closed stellar field lines which enter the disc beyond the corotation radius, and those which are open and not loaded with disc material. Read More

Current models of gamma-ray lightcurves in pulsars suffer from large uncertainties on the precise location of particle acceleration and radiation. Here, we present an attempt to alleviate these difficulties by solving for the electromagnetic structure of the oblique magnetosphere, particle acceleration, and the emission of radiation self-consistently, using 3D spherical particle-in-cell simulations. We find that the low-energy radiation is synchro-curvature radiation from the polar-cap regions within the light cylinder. Read More

It has recently been demonstrated that self-consistent particle-in-cell simulations of low-obliquity pulsar magnetospheres in flat spacetime show weak particle acceleration and no pair production near the poles. We investigate the validity of this conclusion in a more realistic spacetime geometry via general-relativistic particle-in-cell simulations of the aligned pulsar magnetospheres with pair formation. We find that the addition of frame-dragging effect makes local current density along the magnetic field larger than the Goldreich-Julian value, which leads to unscreened parallel electric fields and the ignition of a pair cascade. Read More

The interaction of a rotating star's magnetic field with a surrounding plasma disk lies at the heart of many questions posed by neutron stars in X-ray binaries. We consider the opening of stellar magnetic flux due to differential rotation along field lines coupling the star and disk, using a simple model for the disk-opened flux, the torques exerted on the star by the magnetosphere, and the power extracted by the electromagnetic wind. We examine the conditions under which the system enters an equilibrium spin state, in which the accretion torque is instantaneously balanced by the pulsar wind torque alone. Read More

**Affiliations:**

^{1}Berkeley,

^{2}Princeton,

^{3}Princeton

Rotating neutron stars, or pulsars, are plausibly the source of power behind many astrophysical systems, such as gamma-ray bursts, supernovae, pulsar wind nebulae and supernova remnants. In the past several years, 3D numerical simulations made it possible to compute pulsar spindown luminosity from first principles and revealed that oblique pulsar winds are more powerful than aligned ones. However, what causes this enhanced power output of oblique pulsars is not understood. Read More

**Affiliations:**

^{1}Princeton University,

^{2}Princeton University,

^{3}Princeton University

We study diffusive shock acceleration (DSA) of protons and electrons at nonrelativistic, high Mach number, quasiparallel, collisionless shocks by means of self-consistent 1D particle-in-cell simulations. For the first time, both species are found to develop power-law distributions with the universal spectral index $-4$ in momentum space, in agreement with the prediction of DSA. We find that scattering of both protons and electrons is mediated by right-handed circularly polarized waves excited by the current of energetic protons via non-resonant hybrid (Bell) instability. Read More

We formulate a magnetohydrodynamic-particle-in-cell (MHD-PIC) method for describing the interaction between collisionless cosmic ray (CR) particles and a thermal plasma. The thermal plasma is treated as a fluid, obeying equations of ideal MHD, while CRs are treated as relativistic Lagrangian particles subject to the Lorentz force. Backreaction from CRs to the gas is included in the form of momentum and energy feedback. Read More

We study the linear stability of weakly magnetized differentially rotating plasmas in both collisionless kinetic theory and Braginskii's theory of collisional, magnetized plasmas. We focus on the very weakly magnetized limit that is important for understanding how astrophysical magnetic fields originate and are amplified at high redshift. We show that the single instability of fluid theory - the magnetorotational instability mediated by magnetic tension - is replaced by two distinct instabilities, one associated with ions and one with electrons. Read More

We present first-principles relativistic particle-in-cell simulations of the oblique pulsar magnetosphere with pair formation. The magnetosphere starts to form with particles extracted from the surface of the neutron star. These particles are accelerated by surface electric fields and emit photons capable of producing electron-positron pairs. Read More

The equatorial current sheet in pulsar magnetospheres is often regarded as an ideal site for particle acceleration via relativistic reconnection. Using 2D spherical particle-in-cell simulations, we investigate particle acceleration in the axisymmetric pulsar magnetosphere as a function of the injected plasma multiplicity and magnetization. We observe a clear transition from a highly charge-separated magnetosphere for low plasma injection with little current and spin-down power, to a nearly force-free solution for high plasma multiplicity characterized by a prominent equatorial current sheet and high spin-down power. Read More

**Affiliations:**

^{1}Princeton University,

^{2}Princeton University,

^{3}Princeton University

**Category:**High Energy Astrophysical Phenomena

We use kinetic hybrid simulations (kinetic ions - fluid electrons) to characterize the fraction of ions that are accelerated to non-thermal energies at non-relativistic collisionless shocks. We investigate the properties of the shock discontinuity and show that shocks propagating almost along the background magnetic field (quasi-parallel shocks) reform quasi-periodically on ion cyclotron scales. Ions that impinge on the shock when the discontinuity is the steepest are specularly reflected. Read More

**Affiliations:**

^{1}Princeton University,

^{2}Princeton University

**Category:**High Energy Astrophysical Phenomena

We use large hybrid (kinetic protons-fluid electrons) simulations to investigate the transport of energetic particles in self-consistent electromagnetic configurations of collisionless shocks. In previous papers of this series, we showed that ion acceleration may be very efficient (up to $10-20\%$ in energy), and outlined how the streaming of energetic particles amplifies the upstream magnetic field. Here, we measure particle diffusion around shocks with different strengths, finding that the mean free path for pitch-angle scattering of energetic ions is comparable with their gyroradii calculated in the self-generated turbulence. Read More

**Affiliations:**

^{1}Princeton University,

^{2}Princeton University

We use large hybrid simulations to study ion acceleration and generation of magnetic turbulence due to the streaming of particles that are self-consistently accelerated at non-relativistic shocks. When acceleration is efficient, we find that the upstream magnetic field is significantly amplified. The total amplification factor is larger than 10 for shocks with Alfv\'enic Mach number $M=100$, and scales with the square root of $M$. Read More

**Affiliations:**

^{1}Harvard,

^{2}Princeton

In magnetized astrophysical outflows, the dissipation of field energy into particle energy via magnetic reconnection is often invoked to explain the observed non-thermal signatures. By means of two- and three-dimensional particle-in-cell simulations, we investigate anti-parallel reconnection in magnetically-dominated electron-positron plasmas. Our simulations extend to unprecedentedly long temporal and spatial scales, so we can capture the asymptotic state of the system beyond the initial transients, and without any artificial limitation by the boundary conditions. Read More

**Affiliations:**

^{1}Princeton University,

^{2}Princeton University

**Category:**High Energy Astrophysical Phenomena

We perform first-principles relativistic particle-in-cell simulations of aligned pulsar magnetosphere. We allow free escape of particles from the surface of a neutron star and continuously populate the magnetosphere with neutral pair plasma to imitate pair production. As pair plasma supply increases, we observe the transition from a charge-separated electrosphere solution with trapped plasma and no spin-down to a solution close to the ideal force-free magnetosphere with electromagnetically-dominated pulsar wind. Read More

**Affiliations:**

^{1}Princeton University,

^{2}Princeton University

**Category:**High Energy Astrophysical Phenomena

We use 2D and 3D hybrid (kinetic ions - fluid electrons) simulations to investigate particle acceleration and magnetic field amplification at non-relativistic astrophysical shocks. We show that diffusive shock acceleration operates for quasi-parallel configurations (i.e. Read More

The afterglow emission from gamma-ray bursts (GRBs) is usually interpreted as
synchrotron radiation from electrons accelerated at the GRB external shock,
that propagates with relativistic velocities into the magnetized interstellar
medium. By means of multi-dimensional particle-in-cell simulations, we
investigate the acceleration performance of weakly magnetized relativistic
shocks, in the magnetization range 0

**Affiliations:**

^{1}Princeton,

^{2}Princeton,

^{3}Princeton

The current state of the art in pulsar magnetosphere modeling assumes the force-free limit of magnetospheric plasma. This limit retains only partial information about plasma velocity and neglects plasma inertia and temperature. We carried out time-dependent 3D relativistic magnetohydrodynamic (MHD) simulations of oblique pulsar magnetospheres that improve upon force-free by retaining the full plasma velocity information and capturing plasma heating in strong current layers. Read More

The magnetosphere of a rotating pulsar naturally develops a current sheet beyond the light cylinder (LC). Magnetic reconnection in this current sheet inevitably dissipates a nontrivial fraction of the pulsar spin-down power within a few LC radii. We develop a basic physical picture of reconnection in this environment and discuss its implications for the observed pulsed gamma-ray emission. Read More

**Authors:**Wen Fu

^{1}, Edison P. Liang

^{2}, Milad Fatenejad

^{3}, Donald Q. Lamb

^{4}, Michael Grosskopf

^{5}, Hye-Sook Park

^{6}, Bruce Remington

^{7}, Anatoly Spitkovsky

^{8}

**Affiliations:**

^{1}Rice,

^{2}Rice,

^{3}U. Chicago,

^{4}U. Chicago,

^{5}U. Michigan,

^{6}LLNL,

^{7}LLNL,

^{8}Princeton

Supersonic plasma outflows driven by multi-beam, high-energy lasers, such as Omega and NIF, have been and will be used as platforms for a variety of laboratory astrophysics experiments. Here we propose a new way of launching high density and high velocity, plasma jets using multiple intense laser beams in a hollow ring formation. We show that such jets provide a more flexible and versatile platform for future laboratory astrophysics experiments. Read More

By means of two- and three-dimensional particle-in-cell simulations, we investigate the process of driven magnetic reconnection at the termination shock of relativistic striped flows. In pulsar winds and in magnetar-powered relativistic jets, the flow consists of stripes of alternating magnetic field polarity, separated by current sheets of hot plasma. At the wind termination shock, the flow compresses and the alternating fields annihilate by driven magnetic reconnection. Read More

We investigate guide-field magnetic reconnection and particle acceleration in relativistic pair plasmas with three-dimensional particle-in-cell (PIC) simulations of a kinetic-scale current sheet in a periodic geometry at low magnetizations. The tearing instability is the dominant mode in the current sheet for all guide field strengths, while the linear kink mode is less important even without guide field. Oblique modes seem to be suppressed entirely. Read More

The magnetorotational instability (MRI) is a crucial mechanism of angular momentum transport in a variety of astrophysical accretion disks. In systems accreting at well below the Eddington rate, such as the central black hole in the Milky Way (Sgr A*), the rate of Coulomb collisions between particles is very small, making the disk evolve essentially as a collisionless plasma. We present a nonlinear study of the collisionless MRI using first-principles particle-in-cell (PIC) plasma simulations. Read More

Magnetospheres of pulsars are thought to be filled with plasma, and variations in plasma supply can affect both pulsar emission properties and spin-down rates. A number of recently discovered "intermittent" pulsars switch between two distinct states: an "on", radio-loud state, and an "off", radio-quiet state. Spin-down rates in the two states differ by a large factor, $\sim 1. Read More

**Affiliations:**

^{1}Princeton University,

^{2}Princeton University

**Category:**High Energy Astrophysical Phenomena

The relativistic wind of obliquely-rotating pulsars consists of toroidal stripes of opposite magnetic field polarity, separated by current sheets of hot plasma. By means of two- and three-dimensional particle-in-cell simulations, we investigate particle acceleration and magnetic field dissipation at the termination shock of a relativistic striped wind. At the shock, the flow compresses and the alternating fields annihilate by driven magnetic reconnection. Read More

The current state of the art in the modeling of pulsar magnetospheres invokes either the vacuum or force-free limits for the magnetospheric plasma. Neither of these limits can simultaneously account for both the plasma currents and the accelerating electric fields that are needed to explain the morphology and spectra of high-energy emission from pulsars. To better understand the structure of such magnetospheres, we combine accelerating fields and force-free solutions by considering models of magnetospheres filled with resistive plasma. Read More

Electron acceleration to non-thermal, ultra-relativistic energies (~ 10-100 TeV) is revealed by radio and X-ray observations of shocks in young supernova remnants (SNRs). The diffusive shock acceleration (DSA) mechanism is usually invoked to explain this acceleration, but the way in which electrons are initially energized or 'injected' into this acceleration process starting from thermal energies is an unresolved problem. In this paper we study the initial acceleration of electrons in non-relativistic shocks from first principles, using two- and three-dimensional particle-in-cell (PIC) plasma simulations. Read More

**Affiliations:**

^{1}Princeton University,

^{2}Princeton University

**Category:**High Energy Astrophysical Phenomena

We investigate shock structure and particle acceleration in relativistic magnetized collisionless electron-ion shocks by means of 2.5D particle-in-cell simulations with ion-to-electron mass ratios (m_i/m_e) ranging from 16 to 1000. We explore a range of inclination angles between the pre-shock magnetic field and the shock normal. Read More

The strong variability of magnetic central engines of AGN and GRBs may result in highly intermittent strongly magnetized relativistic outflows. We find a new magnetic acceleration mechanism for such impulsive flows that can be much more effective than the acceleration of steady-state flows. This impulsive acceleration results in kinetic-energy-dominated flows at astrophysically relevant distances from the central source. Read More

**Affiliations:**

^{1}Princeton,

^{2}Princeton

**Category:**High Energy Astrophysical Phenomena

(Abridged) X-ray observations of synchrotron rims in supernova remnant (SNR) shocks show evidence of strong magnetic field amplification (a factor of ~100 between the upstream and downstream medium). This amplification may be due to plasma instabilities driven by shock-accelerated cosmic rays (CRs). One candidate is the cosmic ray current-driven (CRCD) instability (Bell 2004), caused by the electric current of large Larmor radii CRs propagating parallel to the upstream magnetic field. Read More

**Affiliations:**

^{1}Princeton,

^{2}Princeton

**Category:**High Energy Astrophysical Phenomena

Current models of pulsar gamma-ray emission use the magnetic field of a rotating dipole in vacuum as a first approximation to the shape of plasma-filled pulsar magnetosphere. In this paper we revisit the question of gamma-ray light-curve formation in pulsars in order to ascertain the robustness of the "two-pole caustic" (TPC) and "outer gap" (OG) models based on the vacuum magnetic field. We point out an inconsistency in the literature on the use of the relativistic aberration formula, where in several works the vacuum field was treated as known in the instantaneously corotating frame, rather than in the laboratory frame. Read More

**Affiliations:**

^{1}Princeton,

^{2}Princeton

**Category:**High Energy Astrophysical Phenomena

Gamma-ray emission from pulsars is thought to arise from accelerating regions in pulsar's outer magnetosphere. The shape of the light curves is thus sensitive to the details of the magnetic geometry of the magnetosphere. In this work, we show the first calculations of light curves from the more realistic force-free field under the framework of conventional emission models. Read More

**Affiliations:**

^{1}Princeton,

^{2}Princeton

**Category:**High Energy Astrophysical Phenomena

(Abridged) Gamma-ray emission from pulsars has long been modeled using a vacuum dipole field. This approximation ignores changes in the field structure caused by the magnetospheric plasma and strong plasma currents. We present the first results of gamma-ray pulsar light curve modeling using the more realistic field taken from 3D force-free magnetospheric simulations. Read More

We extract synthetic photon spectra from first-principles particle-in-cell simulations of relativistic shocks propagating in unmagnetized pair plasmas. The two basic ingredients for the radiation, namely accelerated particles and magnetic fields, are produced self-consistently as part of the shock evolution. We use the method of Hededal & Nordlund (2005) and compute the photon spectrum via Fourier transform of the electric far-field from a large number of particles, sampled directly from the simulation. Read More

We present a linear analysis of inviscid, incompressible, magnetohydrodynamic (MHD) shallow water systems. In spherical geometry, a generic property of such systems is the existence of five wave modes. Three of them (two magneto-Poincare modes and one magneto-Rossby mode) are previously known. Read More

**Affiliations:**

^{1}Princeton,

^{2}Princeton

**Category:**High Energy Astrophysical Phenomena

Recent particle-in-cell simulations suggest that a large fraction of the energy dissipated in a relativistic shock is deposited into a Maxwellian distribution of electrons that is connected to the high-energy power-law tail. Here, we explore the observational implications of such a mixed thermal-nonthermal particle distribution for the afterglow and prompt emission of gamma-ray bursts. When the Maxwellian component dominates the energy budget, the afterglow lightcurves show a very steep decline phase followed by a more shallow decay when the characteristic synchrotron frequency crosses the observed band. Read More

**Authors:**Dong Lai

^{1}, Marten van Kerkwijk

^{2}, Jon Arons

^{3}, Andrei Beloborodov

^{4}, Edward Brown

^{5}, James Cordes

^{6}, Alice Harding

^{7}, Vicky Kaspi

^{8}, Shri Kulkarni

^{9}, Duncan Lorimer

^{10}, Maura Mclaughlin

^{11}, Roger Romani

^{12}, Anatoly Spitkovsky

^{13}, Tod Strohmayer

^{14}

**Affiliations:**

^{1}Cornell,

^{2}Toronto,

^{3}UCB,

^{4}Columbia,

^{5}MSU,

^{6}Cornell,

^{7}GSFC,

^{8}McGill,

^{9}Caltech,

^{10}WVU,

^{11}WVU,

^{12}Stanford,

^{13}Princeton,

^{14}GSFC

We highlight recent theoretical and observational progress in several areas of neutron star astrophysics, and discuss the prospect for advances in the next decade. Read More

**Affiliations:**

^{1}Princeton,

^{2}Princeton

**Category:**High Energy Astrophysical Phenomena

We investigate shock structure and particle acceleration in relativistic magnetized collisionless pair shocks by means of 2.5D and 3D particle-in-cell simulations. We explore a range of inclination angles between the pre-shock magnetic field and the shock normal. Read More

**Affiliations:**

^{1}Princeton,

^{2}Princeton

**Category:**Astrophysics

The cosmic ray current-driven (CRCD) instability, predicted by Bell (2004), consists of non-resonant, growing plasma waves driven by the electric current of cosmic rays (CRs) that stream along the magnetic field ahead of both relativistic and non-relativistic shocks. Combining an analytic, kinetic model with one-, two-, and three-dimensional particle-in-cell simulations, we confirm the existence of this instability in the kinetic regime and determine its saturation mechanisms. In the linear regime, we show that, if the background plasma is well magnetized, the CRCD waves grow exponentially at the rates and wavelengths predicted by the analytic dispersion relation. Read More

**Affiliations:**

^{1}KU,

^{2}Princeton

**Category:**Astrophysics

We address the question of whether numerical particle-in-cell (PIC) simulations and laboratory laser-plasma experiments can (or will be able to, in the near future) model realistic gamma-ray burst (GRB) shocks. For this, we compare the radiative cooling time, t_cool, of relativistic electrons in the shock magnetic fields to the microscopic dynamical time of collisionless relativistic shocks -- the inverse plasma frequency of protons, omega_pp^{-1}. We obtain that for t_cool*omega_pp^{-1}\lesssim ~few hundred, the electrons cool efficiently at or near the shock jump and are capable of emitiing away a large fraction of the shock energy. Read More

We study relativistic unmagnetized collisionless shocks using unprecedentedly large particle-in-cell simulations of two-dimensional pair plasma. High energy particles accelerated by the shock are found to drive magnetic field evolution on a timescale >10^4 plasma times. Progressively stronger magnetic fields are generated on larger scales in a growing region around the shock. Read More

**Affiliations:**

^{1}Princeton University

**Category:**Astrophysics

We present evidence that relativistic shocks propagating in unmagnetized plasmas can self-consistently accelerate particles. We use long-term two-dimensional particle-in-cell simulations to study the well-developed shock structure in unmagnetized pair plasma. The particle spectrum downstream of such a shock consists of two components: a relativistic Maxwellian, with characteristic temperature set by the upstream kinetic energy of the flow, and a high-energy tail, extending to energies >100 times that of the thermal peak. Read More

**Affiliations:**

^{1}Univ. of California, Berkeley,

^{2}Princeton University,

^{3}Univ. of California, Berkeley

**Category:**Astrophysics

We study the long term evolution of magnetic fields generated by an initially unmagnetized collisionless relativistic $e^+e^-$ shock. Our 2D particle-in-cell numerical simulations show that downstream of such a Weibel-mediated shock, particle distributions are approximately isotropic, relativistic Maxwellians, and the magnetic turbulence is highly intermittent spatially, nonpropagating, and decaying. Using linear kinetic theory, we find a simple analytic form for these damping rates. Read More

**Affiliations:**

^{1}Princeton University

**Category:**Astrophysics

Relativistic collisionless shocks in electron-ion plasma are thought to occur in the afterglow phase of Gamma-Ray Bursts (GRBs), and in other environments where relativistic flows interact with the interstellar medium. A particular regime of shocks in an unmagnetized plasma has generated much interest for GRB applications. In this paper we present ab-initio particle-in-cell simulations of unmagnetized relativistic electron-ion shocks. Read More

**Affiliations:**

^{1}KIPAC, Stanford University

**Category:**Astrophysics

We discuss 3D simulations of relativistic collisionless shocks in electron-positron pair plasmas using the particle-in-cell (PIC) method. The shock structure is mainly controlled by the shock's magnetization ("sigma" parameter). We demonstrate how the structure of the shock varies as a function of sigma for perpendicular shocks. Read More

**Affiliations:**

^{1}KIPAC, Stanford University

**Category:**Astrophysics

Pulsar spindown forms a reliable yet enigmatic prototype for the energy loss processes in many astrophysical objects including accretion disks and back holes. In this paper we review the physics of pulsar magnetospheres, concentrating on recent developments in force-free modeling of the magnetospheric structure. In particular, we discuss a new method for solving the equations of time-dependent force-free relativistic MHD in application to pulsars. Read More

**Affiliations:**

^{1}KIPAC, Stanford University

**Category:**Astrophysics

Magnetospheres of many astrophysical objects can be accurately described by the low-inertia (or "force-free") limit of MHD. We present a new numerical method for solution of equations of force-free relativistic MHD based on the finite-difference time-domain (FDTD) approach with a prescription for handling spontaneous formation of current sheets. We use this method to study the time-dependent evolution of pulsar magnetospheres in both aligned and oblique magnetic geometries. Read More

**Affiliations:**

^{1}Academy of Athens,

^{2}KIPAC, Stanford

**Category:**Astrophysics

We address the issue of electromagnetic pulsar spindown by combining our experience from the two limiting idealized cases which have been studied in great extent in the past: that of an aligned rotator where ideal MHD conditions apply, and that of a misaligned rotator in vacuum. We construct a spindown formula that takes into account the misalignment of the magnetic and rotation axes, and the magnetospheric particle acceleration gaps. We show that near the death line aligned rotators spin down much slower than orthogonal ones. Read More

**Affiliations:**

^{1}Caltech,

^{2}Caltech,

^{3}KIPAC, Stanford

**Category:**Astrophysics

It is generally accepted that magnetic fields generated in the nonlinear development of the transverse Weibel instability provide effective collisionality in unmagnetized collisionless shocks. Recently, extensive two and three dimensional simulations improved our understanding of the growth and saturation of the instability in colliding plasma shells. However, the steady-state structure of the shock wave transition layers remains poorly understood. Read More