Power-law Density Research Articles

Environmental effects on the dynamical evolution of star clusters in turbulent molecular clouds

Context. Star clusters form within giant molecular clouds that are strongly altered by the feedback action of the massive stars, but the cluster still remains embedded in a dense, highly turbulent medium and interactions with ambient structures may modify its dynamical evolution from that expected if it were isolated. Aims. We aim to study coupling mechanisms between the dynamical evolution of the cluster, accelerated by the mass segregation process, with harassment effects caused by the gaseous environment. Methods. We simulated the cluster dynamical evolution combining N-body and hydrodynamic codes within the Astronomical Multipurpose Software Environment (AMUSE). Results. Tidal harassment produces a sparser configuration more rapidly than the isolated reference simulations. The evolution of the asymptotic power-law density distribution exponent also shows substantially different behaviour in the two cases. The background is more effective on clusters in advanced stages of dynamical development.

Spacetime Metrics and Ringdown Waveforms for Galactic Black Holes Surrounded by a Dark Matter Spike

Theoretical models suggest the existence of a dark matter spike surrounding the supermassive black holes at the core of galaxies. The spike density is thought to obey a power law that starts at a few times the black hole horizon radius and extends to a distance, R sp, of the order of a kiloparsec. We use the Tolman–Oppenheimer–Volkoff equations to construct the spacetime metric representing a black hole surrounded by such a dark matter spike. We consider the dark matter to be a perfect fluid, but make no other assumption about its nature. The assumed power-law density provides in principle three parameters with which to work: the power-law exponent γ sp, the external radius R sp, and the spike density at R sp. These in turn determine the total mass of the spike. We focus on Sagittarius A* and M87 for which some theoretical and observational bounds exist on the spike parameters. Using these bounds in conjunction with the metric obtained from the Tolman–Oppenheimer–Volkoff equations, we investigate the possibility of detecting the dark matter spikes surrounding these black holes via the gravitational waves emitted at the ringdown phase of black hole perturbations. Our results suggest that if the spike to black hole mass ratio is roughly constant, greater mass black holes require relatively smaller spike densities to yield potentially observable signals. We find that is unlikely for the spike in M87 to be detected via the ringdown waveform with currently available techniques unless its mass is roughly an order of magnitude larger than existing observational estimates. However, given that the signal increases with black hole mass, dark matter spikes might be observable for more massive galactic black holes in the not too distant future.

Experimental validation of the Kibble-Zurek mechanism on a digital quantum computer

The Kibble-Zurek mechanism (KZM) captures the essential physics of nonequilibrium quantum phase transitions with symmetry breaking. KZM predicts a universal scaling power law for the defect density which is fully determined by the system’s critical exponents at equilibrium and the quenching rate. We experimentally tested the KZM for the simplest quantum case, a single qubit under the Landau-Zener evolution, on an open access IBM quantum computer (IBM-Q). We find that for this simple one-qubit model, experimental data validates the central KZM assumption of the adiabatic-impulse approximation for a well isolated qubit. Furthermore, we report on extensive IBM-Q experiments on individual qubits embedded in different circuit environments and topologies, separately elucidating the role of crosstalk between qubits and the increasing decoherence effects associated with the quantum circuit depth on the KZM predictions. Our results strongly suggest that increasing circuit depth acts as a decoherence source, producing a rapid deviation of experimental data from theoretical unitary predictions.

Mediated Interaction between Ions in Quantum Degenerate Gases.

We explore the interaction between two trapped ions mediated by a surrounding quantum degenerate Bose or Fermi gas. Using perturbation theory valid for weak atom-ion interaction, we show analytically that the interaction mediated by a Bose gas has a power-law behavior for large distances whereas it has a Yukawa form for intermediate distances. For a Fermi gas, the mediated interaction is given by a power law for large density and by a Ruderman-Kittel-Kasuya-Yosida form for low density. For strong atom-ion interaction, we use a diagrammatic theory to demonstrate that the mediated interaction can be a significant addition to the bare Coulomb interaction between the ions, when an atom-ion bound state is close to threshold. Finally, we show that the induced interaction leads to substantial and observable shifts in the ion phonon frequencies.

Testing strong lensing subhalo detection with a cosmological simulation

ABSTRACT Strong gravitational lensing offers a compelling test of the cold dark matter paradigm, as it allows for subhaloes with masses of ∼109 M⊙ and below to be detected. We test commonly used techniques for detecting subhaloes superposed in images of strongly lensed galaxies. For the lens we take a simulated galaxy in a ∼1013 M⊙ halo grown in a high-resolution cosmological hydrodynamical simulation, which we view from two different directions. Though the resolution is high, we note the simulated galaxy still has an artificial core which adds additional complexity to the baryon dominated region. To remove particle noise, we represent the projected galaxy mass distribution by a series of Gaussian profiles which precisely capture the features of the projected galaxy. We first model the lens mass as a (broken) power-law density profile and then search for small haloes. Of the two projections, one has a regular elliptical shape, while the other has distinct deviations from an elliptical shape. For the former, the broken power-law model gives no false positives and correctly recovers the mass of the superposed small halo; however, for the latter we find false positives and the inferred halo mass is overestimated by ∼4–5 times. We then use a more complex model in which the lens mass is decomposed into stellar and dark matter components. In this case, we show that we can capture the simulated galaxy’s complex projected structures and correctly infer the input small halo.

The propagation of relativistic jets in expanding media

ABSTRACT We present a comprehensive analytic model of relativistic jet propagation in expanding homologous media (ejecta). This model covers the entire jet evolution as well as a range of configurations that are relevant to binary neutron star mergers. These include low- and high-luminosity jets, unmagnetized and mildly magnetized jets, time-dependent luminosity jets, and Newtonian and relativistic head velocities. We also extend the existing solution of jets in a static medium to power-law density media with index α < 5. Our model provides simple analytic formulae (calibrated by 3D simulations) for the jet head propagation and breakout times. We find that the system evolution has two main regimes: strong and weak jets. Strong jets start their propagation immediately within the ejecta. Weak jets are unable to penetrate the ejecta at first, and breach it only after the ejecta expands significantly, thus their evolution is independent of the delay between the onset of the ejecta and the jet launching. After enough time, both strong and weak jets approach a common asymptotic phase. We find that a necessary, but insufficient, criterion for the breakout of unmagnetized (weakly magnetized) jets is $E_{j,{\rm iso,tot}} \gtrsim 3[0.4]\, {E_{ej,{\rm tot}}}\left({\, {\theta _{j,0}}}/{0.1{\rm ~rad}}\right)^2$, where Ej, iso, tot is the jet total isotropic equivalent energy, $\, {\theta _{j,0}}$ is its opening angle, and $\, {E_{ej,{\rm tot}}}$ is the ejecta energy. Applying our model to short gamma-ray bursts, we find that there is most likely a large diversity of ejecta mass, where mass ≲10−3 M⊙ (at least along the poles) is common.

Prompt cusp formation from the gravitational collapse of peaks in the initial cosmological density field

ABSTRACT I present an analytic model for the early post-collapse evolution of a spherical density peak on the coherence scale of the initial fluctuations in a universe filled with collisionless and pressure-free ‘dust’. On a time-scale which is short compared to the peak’s collapse time t0, its inner regions settle into an equilibrium cusp with a power-law density profile, ρ ∝ r−12/7. Within this cusp, the circular orbit period P at each radius is related to the enclosed mass M by P = t0(M/Mc)2/3 where Mc is a suitably defined characteristic mass for the initial peak. The relaxation mechanism which produces this cusp gives insight into those which are active in high-resolution simulations of first halo formation in cold or warm dark matter universes, and, indeed, a simple argument suggests that the same power-law index γ = −12/7 should describe the prompt cusps formed during the collapse of generic peaks, independent of any symmetry assumption. Further work is needed to investigate the additional factors required to explain the slightly flatter exponent, γ ≈ −1.5, found in high-resolution numerical simulations of peak collapse.

A lensed radio jet at milliarcsecond resolution I: Bayesian comparison of parametric lens models

ABSTRACT We investigate the mass structure of a strong gravitational lens galaxy at z = 0.350, taking advantage of the milliarcsecond (mas) angular resolution of very long baseline interferometric (VLBI) observations. In the first analysis of its kind at this resolution, we jointly infer the lens model parameters and pixellated radio source surface brightness. We consider several lens models of increasing complexity, starting from an elliptical power-law density profile. We extend this model to include angular multipole structures, a separate stellar mass component, additional nearby field galaxies, and/or a generic external potential. We compare these models using their relative Bayesian log-evidence (Bayes factor). We find strong evidence for angular structure in the lens; our best model is comprised of a power-law profile plus multipole perturbations and external potential, with a Bayes factor of +14984 relative to the elliptical power-law model. It is noteworthy that the elliptical power-law mass distribution is a remarkably good fit on its own, with additional model complexity correcting the deflection angles only at the ∼5 mas level. We also consider the effects of added complexity in the lens model on time-delay cosmography and flux-ratio analyses. We find that an overly simplistic power-law ellipsoid lens model can bias the measurement of H0 by ∼3 per cent and mimic flux ratio anomalies of ∼8 per cent. Our results demonstrate the power of high-resolution VLBI observations to provide strong constraints on the inner density profiles of lens galaxies.

Twisted multilayer nodal superconductors

Twisted bilayers of nodal superconductors were recently proposed as a promising platform to host superconducting phases that spontaneously break time-reversal symmetry. Here we extend this analysis to twisted multilayers, focusing on two high-symmetry stackings with alternating ($\pm \theta$) and constant ($\theta$) twist angles. In analogy to alternating-twist multilayer graphene, the former can be mapped to twisted bilayers with renormalized interlayer couplings, along with a remnant gapless monolayer when the number of layers $L$ is odd. In contrast, the latter exhibits physics beyond twisted bilayers, including the occurrence of `magic angles' characterized by cubic band crossings when $L \mod 4 = 3$. Owing to their power-law divergent density of states, such multilayers are highly susceptible to secondary instabilities. Within a BCS mean-field theory, defined in the continuum and on a lattice, we find that both stackings host chiral topological superconductivity in extended regions of their phase diagrams.

Measuring the thermal and ionization state of the low-z IGM using likelihood free inference

ABSTRACT We present a new approach to measure the power-law temperature density relationship $T=T_0 (\rho/ \bar{\rho })^{\gamma -1}$ and the UV background photoionization rate $\Gamma _{{{{\rm H\, {\small I}}}}{}}$ of the intergalactic medium (IGM) based on the Voigt profile decomposition of the Ly α forest into a set of discrete absorption lines with Doppler parameter b and the neutral hydrogen column density $N_{\rm H\, {\small I}}$. Previous work demonstrated that the shape of the $b-N_{{{{\rm H\, {\small I}}}}{}}$ distribution is sensitive to the IGM thermal parameters T0 and γ, whereas our new inference algorithm also takes into account the normalization of the distribution, i.e. the line-density dN/dz, and we demonstrate that precise constraints can also be obtained on $\Gamma _{{{{\rm H\, {\small I}}}}{}}$. We use density-estimation likelihood-free inference (DELFI) to emulate the dependence of the $b-N_{{{{\rm H\, {\small I}}}}{}}$ distribution on IGM parameters trained on an ensemble of 624 nyx hydrodynamical simulations at z = 0.1, which we combine with a Gaussian process emulator of the normalization. To demonstrate the efficacy of this approach, we generate hundreds of realizations of realistic mock HST/COS data sets, each comprising 34 quasar sightlines, and forward model the noise and resolution to match the real data. We use this large ensemble of mocks to extensively test our inference and empirically demonstrate that our posterior distributions are robust. Our analysis shows that by applying our new approach to existing Ly α forest spectra at z ≃ 0.1, one can measure the thermal and ionization state of the IGM with very high precision ($\sigma _{\log T_0} \sim 0.08$ dex, σγ ∼ 0.06, and $\sigma _{\log \Gamma _{{{{\rm H\, {\small I}}}}{}}} \sim 0.07$ dex).

Effects of CO-dark Gas on Measurements of Molecular Cloud Stability and the Size–Linewidth Relationship

Stars form within molecular clouds, so characterizing the physical states of molecular clouds is key to understanding the process of star formation. Cloud structure and stability are frequently assessed using metrics including the virial parameter and Larson scaling relationships between cloud radius, velocity dispersion, and surface density. Departures from the typical Galactic relationships between these quantities have been observed in low-metallicity environments. The amount of H2 gas in cloud envelopes without corresponding CO emission is expected to be high under these conditions; therefore, this CO-dark gas could plausibly be responsible for the observed variations in cloud properties. We derive simple corrections that can be applied to empirical clump properties (mass, radius, velocity dispersion, surface density, and virial parameter) to account for CO-dark gas in clumps following power-law and Plummer mass density profiles. We find that CO-dark gas is not likely to be the cause of departures from Larson’s relationships in low-metallicity regions, but that virial parameters may be systematically overestimated. We demonstrate that correcting for CO-dark gas is critical for accurately comparing the dynamical state and evolution of molecular clouds across diverse environments.

Static Thin Disks with Power-law Density Profiles * * Dedicated to our teacher, Professor Jiří Bičák, on the occasion of his 80th birthday. For O.S., Jiří's interest in thin disks was, 30 yr ago (Bičák et al. ), the first motivation to study the topic.

The task of finding the potential of a thin circular disk with power-law radial density profile is revisited. The result, given in terms of infinite Legendre-type series in the above reference, has now been obtained in closed form thanks to the method of Conway employing Bessel functions. Starting from a closed-form expression for the potential generated by the elementary density term ρ 2l , we cover more generic—finite solid or infinite annular—thin disks using superposition and/or inversion with respect to the rim. We check several specific cases against the series-expansion form by numerical evaluation at particular locations. Finally, we add a method to obtain a closed-form solution for finite annular disks whose density is of “bump” radial shape, as modeled by a suitable combination of several powers of radius. Density and azimuthal pressure of the disks are illustrated on several plots, together with radial profiles of free circular velocity.

Eccentricity evolution in gaseous dynamical friction

ABSTRACT We analyse how drag forces modify the orbits of objects moving through extended gaseous distributions. We consider how hydrodynamic (surface area) drag forces and dynamical friction (gravitational) drag forces drive the evolution of orbital eccentricity. While hydrodynamic drag forces cause eccentric orbits to become more circular, dynamical friction drag can cause orbits to become more eccentric. We develop a semi-analytic model that accurately predicts these changes by comparing the total work and torque applied to the orbit at periapse and apoapse. We use a toy model of a radial power-law density profile, ρ ∝ r−γ, to determine that there is a critical γ = 3 power index, which separates the eccentricity evolution in dynamical friction: orbits become more eccentric for γ < 3 and circularize for γ > 3. We apply these findings to the infall of a Jupiter-like planet into the envelope of its host star. The hydrostatic envelopes of stars are defined by steep density gradients near the limb and shallower gradients in the interior. Under the influence of gaseous dynamical friction, an infalling object’s orbit will first decrease in eccentricity and then increase. The critical separation that delineates these regimes is predicted by the local density slope and is linearly dependent on polytropic index. More broadly, our findings indicate that binary systems may routinely emerge from common envelope phases with non-zero eccentricities that were excited by the dynamical friction forces that drove their orbital tightening.

Density exponent analysis: gravity-driven steepening of the density profiles of star-forming regions

ABSTRACT The evolution of molecular interstellar clouds is a complex, multiscale process. The power-law density exponent describes the steepness of density profiles, and it has been used to characterize the density structures of the clouds; yet its usage is usually limited to spherically symmetric systems. Importing the Level-Set Method, we develop a new formalism that generates robust maps of a generalized density exponent kρ at every location for complex density distributions. By applying it to high fidelity, high dynamical range map of the Perseus molecular cloud constructed using data from the Herschel and Planck satellites, we find that the density exponent exhibits a surprisingly wide range of variation (−3.5 ≲ kρ ≲ −0.5). Regions at later stages of gravitational collapse are associated with steeper density profiles. Inside a region, gas located in the vicinities of dense structures has very steep density profiles with kρ ≈ −3, which forms because of depletion. This density exponent analysis reveals diverse density structures, forming a coherent picture that gravitational collapse leads to a continued steepening of the density profile. We expect our method to be effective in studying other power law-like density structures, including granular materials and the large-scale structure of the Universe.

Quantifying Feedback from Narrow Line Region Outflows in Nearby Active Galaxies. IV. The Effects of Different Density Estimates on the Ionized Gas Masses and Outflow Rates

Active galactic nuclei (AGN) can launch outflows of ionized gas that may influence galaxy evolution, and quantifying their full impact requires spatially resolved measurements of the gas masses, velocities, and radial extents. We previously reported these quantities for the ionized narrow-line region outflows in six low-redshift AGN, where the gas velocities and extents were determined from Hubble Space Telescope long-slit spectroscopy. However, calculating the gas masses required multicomponent photoionization models to account for radial variations in the gas densities, which span ∼6 orders of magnitude. To simplify this method for larger samples with less spectral coverage, we compare these gas masses with those calculated from techniques in the literature. First, we use a recombination equation with three different estimates for the radial density profiles. These include constant densities, those derived from [S ii], and power-law profiles based on constant values of the ionization parameter (U). Second, we use single-component photoionization models with power-law density profiles based on constant U, and allow U to vary with radius based on the [O iii]/Hβ ratios. We find that assuming a constant density of n H = 102 cm−3 overestimates the gas masses for all six outflows, particularly at small radii where the outflow rates peak. The use of [S ii] marginally matches the total gas masses, but also overestimates at small radii. Overall, single-component photoionization models where U varies with radius are able to best match the gas mass and outflow rate profiles when there are insufficient emission lines to construct detailed models.

Infinite density and relaxation for Lévy walks in an external potential: Hermite polynomial approach.

Lévy walks are continuous-time random-walk processes with a spatiotemporal coupling of jump lengths and waiting times. We here apply the Hermite polynomial method to study the behavior of LWs with power-law walking time density for four different cases. First we show that the known result for the infinite density of an unconfined, unbiased LW is consistently recovered. We then derive the asymptotic behavior of the probability density function (PDF) for LWs in a constant force field, and we obtain the corresponding qth-order moments. In a harmonic external potential we derive the relaxation dynamic of the LW. For the case of a Poissonian walking time an exponential relaxation behavior is shown to emerge. Conversely, a power-law decay is obtained when the mean walking time diverges. Finally, we consider the case of an unconfined, unbiased LW with decaying speed v(τ)=v_{0}/sqrt[τ]. When the mean walking time is finite, a universal Gaussian law for the position-PDF of the walker is obtained explicitly.

Description of the Distribution Law and Non-Linear Dynamics of Growth of Comments Number in News and Blogs Based on the Fokker-Planck Equation

The article considers stationary and dynamic distributions of news by the number of comments. The processing of the observed data showed that static distribution of news by the number of comments relating to that news obeys a power law, and the dynamic distribution (the change in number of comments over time) in some cases has an S-shaped character, and in some cases a more complex two-stage character. This depends on the time interval between the appearance of a comment at the first level and a comment attached to that comment. The power law for the stationary probability density of news distribution by the number of comments can be obtained from the solution of the stationary Fokker-Planck equation, if a number of assumptions are made in its derivation. In particular, we assume that the drift coefficient μ(x) responsible in the Fokker-Planck equation for a purposeful change in the state of system x (x is the current number of comments on that piece of news) linearly depends on the state x, and the diffusion coefficient D(x) responsible for a random change depends quadratically on x. The solution of the unsteady Fokker-Planck differential equation with these assumptions made it possible to obtain an analytical equation for the probability density of transitions between the states of the system per unit of time, which is in good agreement with the observed data, considering the effect of the delay time between the appearance of the first-level comment and the comment on that comment.

A search for planetary companions around 800 pulsars from the Jodrell Bank pulsar timing programme

ABSTRACT We have searched for planetary companions around 800 pulsars monitored at the Jodrell Bank Observatory, with both circular and eccentric orbits of periods between 20 d and 17 yr and inclination-dependent planetary masses from 10−4 to $100\, \mathrm{M}_{\oplus }$. Using a Bayesian framework, we simultaneously model pulsar timing parameters and a stationary noise process with a power-law power spectral density. We put limits on the projected masses of any planetary companions, which reach as low as 1/100th of the mass of the Moon ($\sim 10^{-4}\, \mathrm{M}_{\oplus }$). We find that two-thirds of our pulsars are highly unlikely to host any companions above $2-8\, \mathrm{M}_{\oplus }$. Our results imply that fewer than $0.5{{\ \rm per\ cent}}$ of pulsars could host terrestrial planets as large as those known to orbit PSR B1257+12 ($\sim 4\, \mathrm{M}_{\oplus }$); however, the smaller planet in this system ($\sim 0.02\, \mathrm{M}_{\oplus }$) would be undetectable in $95{{\ \rm per\ cent}}$ of our sample, hidden by both instrumental and intrinsic noise processes, although it is not clear whether such tiny planets could exist in isolation. We detect significant periodicities in 15 pulsars; however, we find that intrinsic quasi-periodic magnetospheric effects can mimic the influence of a planet, and for the majority of these cases we believe this to be the origin of the detected periodicity. Notably, we find that the highly periodic oscillations in PSR B0144+59 are correlated with changes in the pulse profile and therefore can be attributed to magnetospheric effects. We believe the most plausible candidate for planetary companions in our sample is PSR J2007+3120.

Dynamical system analysis of logotropic dark fluid with a power law in the rest-mass energy density

We consider a spatially flat FLRW universe. We assume that it is filled with dark energy in the form of logotropic dark fluid coupled with dark matter in the form of a perfect fluid having a barotropic equation of state. We employ dynamical system tools to obtain a complete qualitative idea of the evolution of such a universe. It is interesting to note that we ought to consider an approximation for the pressure of the logotropic dark fluid in the form of an infinite series so as to be able to construct the autonomous system required for a dynamical system study. This series form provides us with a power law in the rest-mass energy density of the logotropic dark fluid. We compute the critical points of the autonomous system and analyze these critical points by applying linear stability theory. Our analysis reveal a scenario of late-time accelerated universe dominated by the logotropic fluid which behaves as cosmological constant, preceded by an intermediate phase of the Universe dominated by logotropic fluid which behaves as dark matter in the form of perfect fluid. Moreover, it also crosses the phantom divide line.

Statistical strong lensing

Context.Existing samples of strong lenses have been assembled by giving priority to sample size, but this is often at the cost of a complex selection function. However, with the advent of the next generation of wide-field photometric surveys, it might become possible to identify subsets of the lens population with well-defined selection criteria, trading sample size for completeness.Aims.There are two main advantages of working with a complete sample of lenses. First, such completeness makes possible to recover the properties of the general population of galaxies, of which strong lenses are a biased subset. Second, the relative number of lenses and non-detections can be used to further constrain models of galaxy structure. The present work illustrates how to carry out a statistical strong lensing analysis that takes advantage of these features.Methods.I introduce a general formalism for the statistical analysis of a sample of strong lenses with known selection function, and then test it on simulated data. The simulation consists of a population of 105galaxies with an axisymmetric power-law density profile, a population of background point sources, and a subset of ∼103strong lenses, which form a complete sample above an observational cut.Results.The method allows the user to recover the distribution of the galaxy population in Einstein radius and mass density slope in an unbiased way. The number of non-lenses helps to constrain the model when magnification data are not available.Conclusions.Complete samples of lenses are a powerful asset with which to turn precise strong lensing measurements into accurate statements on the properties of the general galaxy population.