arXiv subjects

Uddipan Banik

Publications and source records attributed to Uddipan Banik.

18 recordsLinked to original sources

arXiv2026

Wave interference as the origin of the cyclic magnetorotational dynamo in accretion disks: insights from weakly nonlinear theory and local shearing box simulations

Long-period cyclic reversals of the large-scale magnetic field are a prominent feature of the dynamo associated with the magnetorotational instability (MRI) in accretion disks, but their physical origin remains unclear. We develop a quasilinear theory (QLT) of the MRI dynamo where the electromotive force (emf) is computed from the linear eigenfunctions under the WKB approximation. The emf depends on the mean field $\mathbf{B}$ more generally than standard mean-field closures allow. In the unstratified case, the leading order contribution to the large-scale dynamo is the shear-current effect: the emf depends on the current $\mathbf{J}$ as $\pmb{\varepsilon} = \pmb{\beta}\cdot\mathbf{J}$, with a tensor $\pmb{\beta}(\mathbf{B},t)$ that oscillates with time $t$ and whose off-diagonal components generate the mean field. The oscillations arise from beats between the two branches of eigenfrequencies. Since the beat frequency varies only weakly with wavenumber, the beats remain coherent and drive the long-period butterfly cycle seen in local shearing box simulations. We predict a dominant cycle period $\sim 30{\left(1+a^2\right)}^{1/2}\,t_{\rm orb}$, with $a$ the vertical-to-radial aspect ratio and $t_{\rm orb}$ the orbital period, and an amplitude scaling $\sim a^2$ before saturation at $a\gtrsim 5$. Both trends agree with zero-net-flux unstratified shearing box simulations with Athena++. A carrier-envelope analysis of the simulation spectra shows that the same interference mechanism extends beyond strict QLT, through higher-order linear combinations of the eigenfrequencies, with observed cycles arising from pairwise beats within this spectral network. These results identify coherent interference between nearly degenerate eigenfrequencies as a key mechanism behind large-scale cyclic dynamos, with implications for magnetic variability in protoplanetary disks, X-ray binaries, and AGNs.

astro-ph.HE↗

arXiv2026

Non-thermal particle acceleration in multi-species kinetic plasmas: universal power-law distribution functions and temperature inversion in the solar corona

Non-thermal power-law distribution functions are ubiquitous in astrophysical, space, and laboratory kinetic plasmas, but their origin remains unclear. A related puzzle is the temperature inversion of the solar corona. We show that these phenomena are deeply connected by developing a self-consistent quasilinear theory for electromagnetically driven, unmagnetized kinetic plasmas. The theory yields a multi-species Fokker-Planck equation with drive-induced diffusion from direct acceleration by broad-band turbulent or narrow-band wave-like fields, indirect acceleration by excited waves, and Balescu-Lenard diffusion/drag from Debye-scale fluctuations and Coulomb collisions. For a super-Debye turbulent electric-field spectrum, $|{\bf E}_{\bf k}|^2\propto k^{-\alpha}$, electrons and ions relax toward a universal $f(v)\propto v^{-5}$, or $N(E)\propto E^{-2}$, attractor, equivalent to the high-energy tail of a $\kappa=1.5$ distribution, when $\alpha\ge5$. This universality follows from Debye screening: large-scale fields accelerate unscreened fast particles but not screened slow ones. For shallower spectra, $\alpha<5$, the tail scales as $v^{-\alpha}$; incomplete relaxation and anisotropy also break universality. Anisotropic wave drives yield branch- and spectrum-dependent exponents. Because collisions cannot decelerate suprathermal particles, the tails resist Maxwellianization. In the solar atmosphere, such tails may be generated by chromospheric convection or nanoflares despite collisional and radiative losses. Direct wave heating energizes electrons through Landau-resonant interactions with whistler and electron-cyclotron waves, while ions may be accelerated by turbulent ambipolar fields. Resulting $\kappa\simeq1.5$--$3$ distributions produce an abrupt upper-chromosphere/lower-corona transition and velocity-filtration-driven inverted profiles, yielding coronal temperatures $\sim10^6\,{\rm K}$.

astro-ph.SR↗

arXiv2025

Collisionless relaxation to equilibrium distributions in cold dark matter halos: origin of the Navarro-Frenk-White profile

Collisionless self-gravitating systems such as cold dark matter halos are known to harbor universal density profiles despite the intricate non-linear physics of hierarchical structure formation in the $Λ$CDM paradigm. The origin of such states has been a persistent mystery, particularly because the physics of collisionless relaxation has remained poorly understood. To solve this long-standing problem, we develop a self-consistent quasilinear theory in action-angle space for the collisionless relaxation of inhomogeneous, self-gravitating systems by perturbing the governing Vlasov-Poisson equations. We obtain a quasilinear diffusion equation that describes the secular evolution of the mean coarse-grained distribution function $f_0$ of accreted matter in the fluctuating force field of a spherical isotropic halo. The diffusion coefficient not only depends on the fluctuation power spectrum but also on the evolving potential of the system, which reflects the self-consistency of the problem. Diffusive heating in the pre-assembled halo develops an $r^{-γ}$ inner density cusp, accretion and relaxation in which develops an $r^{-β}$ outer fall-off with $β\approx 5 - 2γ$ in the quasi-steady state. Spherical collapse theory dictates that a quasi-steady outer halo must settle to $β\approx 3$, for which the mass enclosed within a shell barely changes with time. This implies that $γ\approx 1$, which is possible in the quasilinear framework only if (i) the pre-assembled halo harbors an $r^{-γ_{\mathrm{P}}}$ profile with $γ_{\mathrm{P}} \gtrsim 0.5$, (ii) its fluctuations are correlated in time (red noise), and (iii) the initial value of $γ$ is smaller than $1$, implying that the $r^{-1}$ cusp is a neutral equilibrium. We demonstrate for the first time how the Navarro-Frenk-White (NFW) profile emerges as a quasi-steady state of collisionless relaxation.

astro-ph.GA↗

arXiv2025

Not all cores are equal: Phase-space origins of dynamical friction, stalling and buoyancy

Dynamical friction governs the orbital decay of massive perturbers within galaxies and dark matter halos, yet its standard Chandrasekhar formulation fails in systems with cores of (roughly) constant density, where inspiral can halt or even reverse, phenomena known respectively as core stalling and dynamical buoyancy. Although these effects have been observed in simulations, the conditions under which they arise remain unclear. Using high-resolution N-body simulations and analytic insights from kinetic theory, we systematically explore the physical origin of these effects. We demonstrate that the overall distribution function (DF) of the host, not just its central density gradient, determines the efficiency and direction of dynamical friction. Core stalling arises when the perturber encounters a plateau in the DF, either pre-existing or dynamically created through its own inspiral, while buoyancy emerges in systems whose DFs possess an inflection that drives an unstable dipole mode. We show that double power-law density profiles with rapid outer-to-inner slope transitions naturally produce such DF features, which is why structurally similar cores can yield radically different dynamical outcomes. Our results provide a unified framework linking the phase-space structure of galaxies to the fate of embedded massive objects, with direct implications for off-center AGN, the dynamics of nuclear star clusters, and the stalled coalescence of black holes in dwarf galaxies and massive ellipticals.

astro-ph.GA↗

arXiv2025

Universal power-law distribution functions in an electromagnetic kinetic plasma: implications for the inverted temperature profile in the solar corona

We develop a self-consistent quasilinear theory for the relaxation of electromagnetic kinetic plasmas, and demonstrate that the mean distribution functions of both electrons and ions tend to relax to a universal $v^{-5}$ tail. Large-scale electromagnetic (EM) fields efficiently accelerate the unscreened, fast particles but not the screened, slow ones. This non-thermal tail may arise in the solar corona from EM turbulence despite collisions, allowing suprathermal particles to escape the sun's gravity (velocity filtration) and inverting the temperature $(T)$ profile with $T$ rising to $10^6$ K.

astro-ph.SR↗

arXiv2025

A self-consistent quasilinear theory for collisionless relaxation to universal quasi-steady state attractors in cold dark matter halos

Collisionless self-gravitating systems, e.g., cold dark matter halos, harbor universal density profiles despite the intricate non-linear physics of hierarchical structure formation, the origin of which has been a persistent mystery. To solve this problem, we develop a self-consistent quasilinear theory (QLT) in action-angle space for the collisionless relaxation of driven, inhomogeneous, self-gravitating systems by perturbing the governing Vlasov-Poisson equations. We obtain a quasilinear diffusion equation (QLDE) for the secular evolution of the mean distribution function $f_0$ of a halo due to linear fluctuations (induced by random perturbations in the force field) that are collectively dressed by self-gravity, a phenomenon described by the response matrix. Unlike previous studies, we treat collective dressing up to all orders. Well-known halo density profiles $ρ(r)$ commonly observed in $N$-body simulations, including the $r^{-1}$ NFW cusp, an Einasto central core, and the $r^{-1.5}$ prompt cusp, emerge as quasi-steady state attractor solutions of the QLDE. The $r^{-1}$ cusp is a constant flux steady-state solution for a constantly accreting massive halo perturbed by small-scale white noise fluctuations induced by substructure. It is an outcome of the universal nature of collisionless relaxation: lower energy particles attract more particles, gain higher effective mass and get less accelerated by the fluctuating force field. The zero-flux steady state solution for an isolated halo is an $f_0$ that is flat in energy, and the corresponding $ρ(r)$ can either be cored or an $r^{-1.5}$ cusp depending on the inner boundary condition. The latter forms around a central dense object, e.g., a compact subhalo or a black hole. We demonstrate for the first time that these halo profiles emerge as quasi-steady state attractors of collisionless relaxation described by a self-consistent QLT.

astro-ph.GA↗

arXiv2025

The Dipole Instability in Gravitational $N$-body Systems: A Natural Explanation for Lopsidedness and Off-Centered Nuclei in Galaxies

We explore the stability of isotropic, spherical, self-gravitating systems with a double-power law density profile. Systems with rapid transitions between the inner and outer slopes are shown to have an inflection in their isotropic distribution function (DF), where ${\rm d} f/{\rm d} E > 0$, thereby violating Antonov's stability criterion. Using high-resolution $N$-body simulations, we show that the resulting instability causes the growth of a rotating dipole (or $l=1$) mode. The inflection feature in the DF responds to the mode by promoting its growth, driving the instability. The growth of the dipole results in a torque that dislodges the original cusp from its central location, and sets it in motion throughout the central region. Once the mode goes non-linear, it saturates, together with the cusp, into a long-lived soliton (the $l=1$ equivalent of a bar in a disk galaxy), which maintains its sloshing motion through the center of the halo along a slowly precessing, elliptical orbit. Concurrently, the soliton traps increasingly more particles into libration, and the exchange of energy and angular momentum with these trapped particles works towards eroding the bump in the distribution function. We point out similarities between the dipole mode and the bump-on-tail instability in electrostatic plasmas, and highlight a potential connection with core stalling and dynamical buoyancy in systems with a cored density profile. Finally, we discuss the astrophysical implications in terms of lopsidedness and off-center nuclei in galaxies.

astro-ph.GA↗

arXiv2024

Universal non-thermal power-law distribution functions from the self-consistent evolution of collisionless electrostatic plasmas

Distribution functions of collisionless systems are known to show non-thermal power law tails. Interestingly, collisionless plasmas in various physical scenarios, (e.g., the ion population of the solar wind) feature a $v^{-5}$ tail in the velocity ($v$) distribution, whose origin has been a long-standing mystery. We show this power law tail to be a natural outcome of the self-consistent collisionless relaxation of driven electrostatic plasmas. We perform a quasilinear analysis of the perturbed Vlasov-Poisson equations to show that the coarse-grained mean distribution function (DF), $f_0$, follows a quasilinear diffusion equation with a diffusion coefficient $D(v)$ that depends on $v$ through the plasma dielectric constant. If the plasma is isotropically forced on scales much larger than the Debye length with a white noise-like electric field, then $D(v)\sim v^4$ for $σ<v<ω_{\mathrm{P}}/k$, with $σ$ the thermal velocity, $ω_{\mathrm{P}}$ the plasma frequency and $k$ the maximum wavenumber of the perturbation; the corresponding $f_0$, in the quasi-steady state, develops a $v^{-\left(d+2\right)}$ tail in $d$ dimensions ($v^{-5}$ tail in 3D), while the energy ($E$) distribution develops an $E^{-2}$ tail irrespective of the dimensionality of space. Any redness of the noise only alters the scaling in the high $v$ end. Non-resonant particles moving slower than the phase-velocity of the plasma waves ($ω_{\mathrm{P}}/k$) experience a Debye-screened electric field, and significantly less (power law suppressed) acceleration than the near-resonant particles. Thus, a Maxwellian DF develops a power law tail. The Maxwellian core ($v<σ$) eventually also heats up, but over a much longer timescale than that over which the tail forms. We definitively show that self-consistency (ignored in test-particle treatments) is crucial for the development of the universal $v^{-5}$ tail.

astro-ph.SR↗

arXiv2024

Relaxation of weakly collisional plasma: continuous spectra, discrete eigenmodes, and the decay of echoes

The relaxation of a weakly collisional plasma, which is of fundamental interest to laboratory and astrophysical plasmas, can be described by the Boltzmann-Poisson equations with the Lenard-Bernstein collision operator. We perform a perturbative analysis of these equations, and obtain exact analytic solutions that resolve long-standing controversies regarding the impact of weak collisions on the continuous spectra, discrete Landau eigenmodes, and the decay of plasma echoes. We retain both damping and diffusion terms in the collision operator. We find that the linear response is a temporal convolution of a continuum that depends on the continuous velocities of particles (crucial for the plasma echo) and discrete modes that describe coherent oscillations of the entire system. The discrete modes are exponentially damped over time due to collective effects or wave-particle interactions (Landau damping) as well as collisional dissipation. The continuum is also damped by collisions, but somewhat differently. Up to a collision time, the inverse of the collision frequency $ν_{\mathrm{c}}$, the continuum decay is driven by the diffusion of particle velocities and occurs cubic exponentially over a timescale $\sim ν^{-1/3}_{\mathrm{c}}$. After a collision time, however, the continuum decay is driven by the damping of velocities and diffusion of positions, and occurs exponentially over a timescale $\sim ν_{\mathrm{c}}$. This slow exponential decay damps perturbations the most on scales $λ$ comparable to the mean free path $λ_{\mathrm{c}}$, but very slowly on larger scales. This establishes local thermal equilibrium, the essence of the fluid limit, and enhances the detectability of the plasma echo. The long-term decay is driven by the discrete modes for $λ<λ_{\mathrm{c}}$, but, by the slowly decaying continuum and the least damped mode for $λ>λ_{\mathrm{c}}$.

physics.plasm-ph↗

arXiv2024

Pushing the Frontiers of Non-equilibrium Dynamics of Collisionless and Weakly Collisional Self-gravitating Systems

In the standard cosmological paradigm, structure formation occurs via gravitational encounters and mergers between galaxies and dark matter halos. These collisionless self-gravitating systems therefore prevail in a state of non-equilibrium or quasi-equilibrium at best. Recent observations show that even our own Milky Way galaxy harbors non-equilibrium features. This calls for a shift of gear from the standard equilibrium galactic dynamics to the less explored non-equilibrium dynamics. This dissertation presents novel theories to describe the relaxation/equilibration of perturbed galaxies (via phase-mixing, Landau damping, etc.) in the impulsive, adiabatic and near-resonant regimes, as well as the back reaction of the host galaxy response on the perturber, resulting in its secular evolution (dynamical friction). First, we present a non-perturbative treatment of penetrating impulsive encounters between galaxies, a generalization of the standard theory which only works for distant encounters. Next, a general perturbative formalism for the phase-mixing of the response of disk galaxies to external perturbations (e.g., satellite impacts) is presented, which describes the formation and evolution of non-equilibrium features called phase-spirals akin to those discovered in our Milky Way galaxy by Gaia. Finally, we present a self-consistent perturbative theory and a non-perturbative orbit-based treatment of the near-resonant galaxy response and dynamical friction. These theories, for the first time, explain the origin of dynamical buoyancy and core-stalling, phenomena observed in $N$-body simulations of the dynamical friction of massive perturbers in cored galaxies that are unexplained in the standard Chandrasekhar and resonance theories. These processes have profound astrophysical implications, e.g., they can stall and potentially choke supermassive black hole mergers in cored galaxies.

astro-ph.GA↗

arXiv2023

A Comprehensive Perturbative Formalism for Phase Mixing in Perturbed Disks. II. Phase Spirals in an Inhomogeneous Disk Galaxy with a Non-responsive Dark Matter Halo

We develop a linear perturbative formalism to compute the response of an inhomogeneous stellar disk embedded in a non-responsive dark matter halo to perturbations like bars, spiral arms and satellite galaxy encounters. Without self-gravity to reinforce it, the response of a Fourier mode phase mixes away due to an intrinsic spread in the vertical ($Ω_z$), radial ($Ω_r$) and azimuthal ($Ω_ϕ$) frequencies, giving rise to local phase-space spirals. Collisional diffusion due to scattering of stars by structures like giant molecular clouds causes super-exponential damping of the phase-spiral amplitude. The $z-v_z$ phase-spiral is 1-armed (2-armed) for vertically anti-symmetric (symmetric) bending (breathing) modes. Only transient perturbations with timescales ($τ_{\mathrm{P}}$) comparable to the vertical oscillation period ($τ_z \sim 1/Ω_z$) trigger $z-v_z$ phase-spirals. Each $(n,l,m)$ mode of the response to impulsive ($τ_{\mathrm{P}}<τ=1/(nΩ_z+lΩ_r+mΩ_ϕ)$) perturbations is power law ($\sim τ_{\mathrm{P}}/τ$) suppressed, but that to adiabatic ($τ_{\mathrm{P}}>τ$) perturbations is exponentially weak ($\sim \exp{\left[-\left(τ_{\mathrm{P}}/τ\right)^α\right]}$) except resonant ($τ\to \infty$) modes. Slower ($τ_{\mathrm{P}}>τ_z$) perturbations, e.g., distant encounters with satellite galaxies, induce stronger bending modes. If the Gaia phase-spiral was triggered by a satellite, Sagittarius is the leading contender as it dominates the Solar neighborhood response of the Milky Way disk to satellite encounters. However, survival against collisional damping necessitates that the impact occurred within $\sim 0.6-0.7$ Gyr ago. We discuss how the detailed galactic potential dictates the phase-spiral shape: phase mixing occurs slower and phase-spirals are less wound in the outer disk and in presence of an ambient halo.

astro-ph.GA↗

arXiv2022

A Comprehensive Perturbative Formalism for Phase-Mixing in Perturbed Disks. I. Phase spirals in an Infinite, Isothermal Slab

Galactic disks are highly responsive systems that often undergo external perturbations and subsequent collisionless equilibration, predominantly via phase-mixing. We use linear perturbation theory to study the response of infinite isothermal slab analogues of disks to perturbations with diverse spatio-temporal characteristics. Without self-gravity of the response, the dominant Fourier modes that get excited in a disk are the bending and breathing modes, which, due to vertical phase-mixing, trigger local phase-space spirals that are one- and two-armed, respectively. We demonstrate how the lateral streaming motion of slab stars causes phase spirals to damp out over time. The ratio of the perturbation timescale ($τ_{\mathrm{P}}$) to the local, vertical oscillation time ($τ_z$) ultimately decides which of the two modes is excited. Faster, more impulsive ($τ_{\mathrm{P}} < τ_z$) and slower, more adiabatic ($τ_{\mathrm{P}} > τ_z$) perturbations excite stronger breathing and bending modes, respectively, although the response to very slow perturbations is exponentially suppressed. For encounters with satellite galaxies, this translates to more distant and more perpendicular encounters triggering stronger bending modes. We compute the direct response of the Milky Way disk to several of its satellite galaxies, and find that recent encounters with all of them excite bending modes in the Solar neighborhood. The encounter with Sagittarius triggers a response that is at least $1-2$ orders of magnitude larger than that due to any other satellite, including the Large Magellanic Cloud. We briefly discuss how ignoring the presence of a dark matter halo and the self-gravity of the response might impact our conclusions.

astro-ph.GA↗

arXiv2021

Dynamical Friction, Buoyancy and Core-Stalling -- I. A Non-perturbative Orbit-based Analysis

We examine the origin of dynamical friction using a non-perturbative, orbit-based approach. Unlike the standard perturbative approach, in which dynamical friction arises from the LBK torque due to pure resonances, this alternative, complementary view nicely illustrates how a massive perturber significantly changes the energies and angular momenta of field particles on near-resonant orbits, with friction arising from an imbalance between particles that gain energy and those that lose energy. We treat dynamical friction in a spherical host system as a restricted three-body problem. This treatment is applicable in the `slow' regime, in which the perturber sinks slowly and the standard perturbative framework fails due to the onset of non-linearities. Hence it is especially suited to investigate the origin of core-stalling: the cessation of dynamical friction in central constant-density cores. We identify three different families of near-co-rotation-resonant orbits that dominate the contribution to dynamical friction. Their relative contribution is governed by the Lagrange points (fixed points in the co-rotating frame). In particular, one of the three families, which we call Pac-Man orbits because of their appearance in the co-rotating frame, is unique to cored density distributions. When the perturber reaches a central core, a bifurcation of the Lagrange points drastically changes the orbital make-up, with Pac-Man orbits becoming dominant. In addition, due to relatively small gradients in the distribution function inside a core, the net torque from these Pac-Man orbits becomes positive (enhancing), thereby effectuating a dynamical buoyancy. We argue that core stalling occurs where this buoyancy is balanced by friction.

astro-ph.GA↗

arXiv2021

A Self-Consistent, Time-Dependent Treatment of Dynamical Friction: New Insights regarding Core Stalling and Dynamical Buoyancy

Dynamical friction is typically regarded a secular process, in which the subject ('perturber') evolves very slowly (secular approximation), and has been introduced to the host over a long time (adiabatic approximation). These assumptions imply that dynamical friction arises from the LBK torque with non-zero contribution only from pure resonance orbits. However, dynamical friction is only of astrophysical interest if its timescale is shorter than the age of the Universe. In this paper we therefore relax the adiabatic and secular approximations. We first derive a generalized LBK torque, which reduces to the LBK torque in the adiabatic limit, and show that it gives rise to transient oscillations due to non-resonant orbits that slowly damp out, giving way to the LBK torque. This is analogous to how a forced, damped oscillator undergoes transients before settling to a steady state, except that here the damping is due to phase mixing rather than dissipation. Next, we present a self-consistent treatment, that properly accounts for time-dependence of the perturber potential and circular frequency (memory effect), which we use to examine orbital decay in a cored galaxy. We find that the memory effect results in a phase of accelerated, super-Chandrasekhar friction before the perturber stalls at a critical radius, $R_{\mathrm{crit}}$, in the core (core-stalling). Inside of $R_{\mathrm{crit}}$ the torque flips sign, giving rise to dynamical buoyancy, which counteracts friction and causes the perturber to stall. This phenomenology is consistent with $N$-body simulations, but has thus far eluded proper explanation.

astro-ph.GA↗

arXiv2021

A Fully General, Non-Perturbative Treatment of Impulsive Heating

Impulsive encounters between astrophysical objects are usually treated using the distant tide approximation (DTA) for which the impact parameter, $b$, is assumed to be significantly larger than the characteristic radii of the subject, $r_{\mathrm{S}}$, and the perturber, $r_{\mathrm{P}}$. The perturber potential is then expanded as a multipole series and truncated at the quadrupole term. When the perturber is more extended than the subject, this standard approach can be extended to the case where $r_{\mathrm{S}} \ll b < r_{\mathrm{P}}$. However, for encounters with $b$ of order $r_{\mathrm{S}}$ or smaller, the DTA typically overpredicts the impulse, $Δ\mathbf{v}$, and hence the internal energy change of the subject, $ΔE_{\mathrm{int}}$. This is unfortunate, as these close encounters are the most interesting, potentially leading to tidal capture, mass stripping, or tidal disruption. Another drawback of the DTA is that $ΔE_{\mathrm{int}}$ is proportional to the moment of inertia, which diverges unless the subject is truncated or has a density profile that falls off faster than $r^{-5}$. To overcome these shortcomings, this paper presents a fully general, non-perturbative treatment of impulsive encounters which is valid for any impact parameter, and not hampered by divergence issues, thereby negating the necessity to truncate the subject. We present analytical expressions for $Δ\mathbf{v}$ for a variety of perturber profiles, apply our formalism to both straight-path encounters and eccentric orbits, and discuss the mass loss due to tidal shocks in gravitational encounters between equal mass galaxies.

astro-ph.GA↗

arXiv2018

Constraining the mass density of free-floating black holes using razor-thin lensing arcs

Strong lensing of active galactic nuclei in the radio can result in razor-thin arcs, with a thickness of less than a milli-arcsecond, if observed at the resolution achievable with very long baseline interferometry (VLBI). Such razor-thin arcs provide a unique window on the coarseness of the matter distribution between source and observer. In this paper, we investigate to what extent such razor-thin arcs can constrain the number density and mass function of `free-floating' black holes, defined as black holes that do not, or no longer, reside at the centre of a galaxy. These can be either primordial in origin or arise as by-products of the evolution of super-massive black holes in galactic nuclei. When sufficiently close to the line of sight, free-floating black holes cause kink-like distortions in the arcs, which are detectable by eye in the VLBI images as long as the black hole mass exceeds $\sim 1000$ Solar masses. Using a crude estimate for the detectability of such distortions, we analytically compute constraints on the matter density of free-floating black holes resulting from null-detections of distortions along a realistic, fiducial arc, and find them to be comparable to those from quasar milli-lensing. We also use predictions from a large hydrodynamical simulation for the demographics of free-floating black holes that are not primordial in origin, and show that their predicted mass density is roughly four orders of magnitude below the constraints achievable with a single razor-thin arc.

astro-ph.CO↗

arXiv2018

Exact results in Floquet coin toss for driven integrable models

We study an integrable Hamiltonian reducible to free fermions which is subjected to an imperfect periodic driving with the amplitude of driving (or kicking) randomly chosen from a binary distribution like a coin-toss problem. The randomness present in the driving protocol destabilises the periodic steady state, reached in the limit of perfectly periodic driving, leading to a monotonic rise of the stroboscopic residual energy with the number of periods ($N$). We establish that a minimal deviation from the perfectly periodic driving would always result in a {\it bounded} heating up of the system with $N$ to an asymptotic finite value. Remarkably, exploiting the completely uncorrelated nature of the randomness and the knowledge of the stroboscopic Floquet operator in the perfectly periodic situation, we provide an exact analytical formalism to derive the disorder averaged expectation value of the residual energy through a {\it disorder operator}. This formalism not only leads to an immense numerical simplification, but also enables us to derive an exact analytical form for the residual energy in the asymptotic limit which is universal, i.e, independent of the bias of coin-toss and the protocol chosen. Furthermore, this formalism clearly establishes the nature of the monotonic growth of the residual energy at intermediate $N$ while clearly revealing the possible non-universal behaviour of the same.

cond-mat.stat-mech↗

arXiv2017

Self-gravitating fluid systems and galactic dark matter

We study gravitational collapse with anisotropic pressures, whose end stage can mimic space-times that are seeded by galactic dark matter. To this end, we identify a class of space-times (with conical defects) that can arise out of such a collapse process, and admit stable circular orbits at all radial distances. These have a naked singularity at the origin. An example of such a space-time is seen to be the Bertrand space-time discovered by Perlick, that admits closed, stable orbits at all radii. Using relativistic two- fluid models, we show that our galactic space-times might indicate exotic matter, i.e one of the component fluids may have negative pressure for a certain asymptotic fall off of the associated mass density, in the Newtonian limit. We complement this analysis by studying some simple examples of Newtonian two-fluid systems, and compare this with the Newtonian limit of the relativistic systems considered.

astro-ph.GA↗