Instability Time Scale Research Articles

Linear Stability Analysis of a Magnetic Rotating Disk with Ohmic Dissipation and Ambipolar Diffusion

Abstract We perform a linear analysis of the stability of isothermal, rotating, magnetic, self-gravitating sheets that are weakly ionized. The magnetic field and rotation axis are perpendicular to the sheet. We include a self-consistent treatment of thermal pressure, gravitational, rotational, and magnetic (pressure and tension) forces together with two nonideal magnetohydrodynamic (MHD) effects (ohmic dissipation and ambipolar diffusion) that are treated together for their influence on the properties of gravitational instability for a rotating sheetlike cloud or disk. Our results show that there is always a preferred length scale and associated minimum timescale for gravitational instability. We investigate their dependence on important dimensionless free parameters of the problem: the initial normalized mass-to-flux ratio μ 0, the rotational Toomre parameter Q, the dimensionless ohmic diffusivity η ˜ OD , 0 , and the dimensionless neutral–ion collision time τ ˜ ni , 0 , which is a measure of the ambipolar diffusivity. One consequence of η ˜ OD , 0 is that there is a maximum preferred length scale of instability that occurs in the transcritical (μ 0 ≳ 1) regime, qualitatively similar to the effect of τ ˜ ni , 0 , but with quantitative differences. The addition of rotation leads to a generalized Toomre criterion (that includes a magnetic dependence) and modified length scales and timescales for collapse. When nonideal MHD effects are also included, the Toomre criterion reverts back to the hydrodynamic value. We apply our results to protostellar disk properties in the early embedded phase and find that the preferred scale of instability can significantly exceed the thermal (Jeans) scale and the peak preferred fragmentation mass is likely to be ∼10–90 M Jup.

Semicontinuous paleomagnetic record of the last 1 Ma from radiometrically dated igneous rocks (Trans-Mexican Volcanic Belt and surrounding areas)

The radiometric data available in the Trans-Mexican Volcanic Belt enables a quasi-continuous record of the Earth's magnetic field over the last million years to be obtained. Here, we analyze 149 well-defined paleomagnetic directions supported by an equal number of isotope ages. Eleven new paleomagnetic directions from the Tacambaro-Puruaran area (the Michoacán Guanajuato Volcanic Field) are incorporated into the database. Global mean paleomagnetic directions are calculated for one Ma after discarding transitional lavas. The mean direction agrees with the expected paleomagnetic directions obtained from the Pliocene-Quaternary reference poles within the range of uncertainty. The secular variation rate estimated through the scattering of the calculated virtual geomagnetic poles, and the inclination anomaly, both agree with recently reported latitudinal distribution models. An interesting feature of the paleomagnetic direction compilation is the possible evidence of relatively short geomagnetic events or excursions within Matuyama and Brunhes chrons, which may help to refine the geomagnetic instability time scale (GITS).

Lyapunov exponent, ISCO and Kolmogorov\u2013Senai entropy for Kerr\u2013Kiselev black hole

Geodesic motion has significant characteristics of space-time. We calculate the principle Lyapunov exponent (LE), which is the inverse of the instability timescale associated with this geodesics and Kolmogorov–Senai (KS) entropy for our rotating Kerr–Kiselev (KK) black hole. We have investigate the existence of stable/unstable equatorial circular orbits via LE and KS entropy for time-like and null circular geodesics. We have shown that both LE and KS entropy can be written in terms of the radial equation of innermost stable circular orbit (ISCO) for time-like circular orbit. Also, we computed the equation marginally bound circular orbit, which gives the radius (smallest real root) of marginally bound circular orbit (MBCO). We found that the null circular geodesics has larger angular frequency than time-like circular geodesics (Q_o > Q_{sigma }). Thus, null-circular geodesics provides the fastest way to circulate KK black holes. Further, it is also to be noted that null circular geodesics has shortest orbital period (T_{photon}< T_{ISCO}) among the all possible circular geodesics. Even null circular geodesics traverses fastest than any stable time-like circular geodesics other than the ISCO.

The Shannon entropy: An efficient indicator of dynamical stability

In this work it is shown that the Shannon entropy is an efficient dynamical indicator that provides a direct measure of the diffusion rate and thus a time-scale for the instabilities arising when dealing with chaos. Its computation just involves the solution of the Hamiltonian flow, the variational equations are not required. After a review of the theory behind this approach, two particular applications are presented; a 4D symplectic map and the exoplanetary system HD 181433, approximated by the Planar Three Body Problem. Successful results are obtained for instability time-scales when compared with direct long range integrations (N-body or just iterations). Comparative dynamical maps reveal that this novel technique provides much more dynamical information than a classical chaos indicator.

Gravitational Instability of a Magnetic Rotating Disk with Ohmic Dissipation and Ambipolar Diffusion

Abstract We perform a linear analysis of the stability of isothermal, rotating, magnetic, self-gravitating sheets that are weakly ionized. We include a self-consistent treatment of thermal pressure, gravitational, rotational, and magnetic (pressure and tension) forces together with two nonideal magnetohydrodynamic (MHD) effects: Ohmic dissipation and ambipolar diffusion. Our results show that there is always a preferred lengthscale and associated minimum timescale for gravitational instability. The addition of rotation leads to a generalized Toomre criterion (that includes a magnetic dependence) and modified lengthscales and timescales for collapse. We show that both the nonideal MHD effects qualitatively behave in a similar way but have quantitative differences. We apply our results to protostellar disk properties in the early embedded phase and find that the preferred scale of instability can significantly exceed the thermal (Jeans) scale and the peak preferred fragmentation mass is likely to be ∼10–90M Jup.

High‐resolution stratigraphy of Quaternary fluvial deposits in the Makó Trough and the Danube‐Tisza Interfluve, Hungary, based on magnetic susceptibility data

High‐resolution stratigraphical architecture of a Quaternary fluvial succession in the Makó Trough and the Danube‐Tisza Interfluve (Pannonian Basin, Hungary) was investigated based on low field magnetic susceptibility (MS) measurements of seven fully cored boreholes, interpreted on the basis of the early postglacial magnetic susceptibility episodes previously described in the Körös and Jászság Basins. To confirm the reliability of the Dévaványa and Vésztő MS records (Körös Basin), the published magnetostratigraphical data were re‐investigated revealing the consequent arrangement of the MS peaks correlated with the Jingbian section and the short‐lived polarity reversals correlated with the Geomagnetic Instability Time Scale. The Quaternary climatic regime in the Körös Basin begins in the late Pliocene at 2.7 Ma. The correlation between the Körös Basin (Dévaványa) and Makó Trough (Mindszent) was confirmed by the multi‐proxy spectral investigation of the Mindszent section, revealing ~100‐ and ~41‐ka cycles in the MS, colour, logged spontaneous potential and resistivity records. Based on MS records of the seven boreholes, the base of the Quaternary can be identified irrespective of the facies, age and climatic phase of the lowermost Quaternary strata. By performing MS and log correlation of 131 boreholes, extended unconformities were detected in the Quaternary profiles in the Danube‐Tisza Interfluve (~1070±10, ~1920±10 and ~2300±10 ka) interpreted as sequence boundaries. Sedimentological and mineralogical data reveal a significant change at ~725–606 ka likely as a response to the ‘mid‐Pleistocene transition’, leading to the multiple branching of the Danube. SEM data revealed that ilmenite is also responsible for the development of the early postglacial magnetic susceptibility episodes. This increases the stratigraphical potential of fluvial successions with catchment area that contain metamorphic rocks. A gradual retreat of permafrost zone determines long‐term temporal trends of the climatically controlled fluvial magnetic susceptibility episodes, causing upward decreasing trends in the time series.

Mitigation of Darrieus–Landau instability effects on turbulent premixed flames

Theoretical considerations on the competition between the most amplified modes for Darrieus–Landau (DL) hydrodynamic instability and turbulence timescales, show that, two extremal regimes can be identified: the instability-dominated and turbulence-dominated regimes. In the latter, also denoted as unified regime, both experiments and numerical simulations give evidence showing how the large scale, cusp-like structures of the flame front surface, typical of DL instability, are hindered by turbulent fluctuations. The result is that quantities such as turbulent flame propagation and front curvature statistics, which in the instability dominated regime are enhanced or modified by the overwhelming presence of hydrodynamic instability, are now mitigated and a unified regime is reached in which the characteristics of DL unstable and stable flame configurations become indistinguishable. In this work we analyze the concealing effects of increasing level of turbulence over the hydrodynamic Darrieus–Landau instability, and we show that, although some global indices such as the skewness of the curvature p.d.f. suggest that a unified regime is reached, others show the persistence of residual differences: in particular, the power spectral density of the flame front curvature. We use both experimental and numerical datasets of stable and unstable (based on linear stability analysis) flames, in conditions ranging from quasi laminar to significantly turbulent regimes.

Geodesic stability and quasi normal modes via Lyapunov exponent for Hayward black hole

We derive proper time Lyapunov exponent [Formula: see text] and coordinate time Lyapunov exponent [Formula: see text] for a regular Hayward class of black hole. The proper time corresponds to [Formula: see text] and the coordinate time corresponds to [Formula: see text], where [Formula: see text] is measured by the asymptotic observers both for Hayward black hole and for special case of Schwarzschild black hole. We compute their ratio as [Formula: see text] for time-like geodesics. In the limit of [Formula: see text] that means for Schwarzschild black hole this ratio reduces to [Formula: see text]. Using Lyapunov exponent, we investigate the stability and instability of equatorial circular geodesics. By evaluating the Lyapunov exponent, which is the inverse of the instability time scale, we show that, in the eikonal limit, the real and imaginary parts of quasi-normal modes (QNMs) is specified by the frequency and instability time scale of the null circular geodesics. Furthermore, we discuss the unstable photon sphere and radius of shadow for this class of black hole.

Black Hole Superradiant Instability from Ultralight Spin-2 Fields.

Ultralight bosonic fields are compelling dark-matter candidates and arise in a variety of beyond standard model scenarios. These fields can tap energy and angular momentum from spinning black holes through superradiant instabilities, during which a macroscopic bosonic condensate develops around the black hole. Striking features of this phenomenon include gaps in the spin-mass distribution of astrophysical black holes and a continuous gravitational-wave (GW) signal emitted by the condensate. So far these processes have been studied in great detail for scalar fields and, more recently, for vector fields. Here we take an important step forward in the black hole superradiance program by computing, analytically, the instability timescale, direct GW emission, and stochastic background, in the case of massive tensor (i.e., spin-2) fields. Our analysis is valid for any black hole spin and for small boson masses. The instability of massive spin-2 fields shares some properties with the scalar and vector cases, but its phenomenology is much richer, for example, there exist multiple modes with comparable instability timescales, and the dominant GW signal is hexadecapolar rather than quadrupolar. Electromagnetic and GW observations of spinning black holes in the mass range M∈(1,10^{10}) M_{⊙} can constrain the mass of a putative spin-2 field in the range 10^{-22}≲m_{b} c^{2}/eV≲10^{-10} . For 10^{-17}≲m_{b} c^{2}/eV≲10^{-15} , the space mission LISA could detect the continuous GW signal for sources at redshift z=20, or even larger.

Superradiance of a global monopole in Reissner\u2013Nordstr\xf6m(\u2013AdS) space-time

In this article, the behavior of a charged and massive scalar field around a global monopole swallowed by a Reissner–Nordström–Anti-de Sitter (RN–AdS) black hole is investigated by considering the Klein–Gordon equation in this geometry. The superradiance phenomenon and instability behavior of the black hole against charged scalar perturbations are studied for both an RN–AdS case and also for an RN black hole surrounded by a reflective mirror, i.e., the black hole bomb case. The effects of the monopole on these cases are discussed analytically and also with the help of several graphs in detail. The monopole charge affects the superradiance threshold frequency and also effects the instability time scale for both cases. The existence of global monopole makes these black holes more stable against superradiance instability.

Time‐dependent plasma transport simulation for the study of edge impurity radiation dynamics with magnetic island in large helical device

AbstractThe dynamics of impurity radiation distribution during detachment transition with edge magnetic island induced by the application of resonant magnetic perturbation (RMP) is studied numerically by solving time‐dependent plasma fluid equations together with impurity and neutral transports in a 2D grid system. Computations provide the appearance of a macroscopic structure in the heat transfer along the island separatrix and outside the island. The resultant parallel temperature gradient generates the plasma flow and the density gradient according to the parallel momentum balance. The resulting plasma flow effectively transports impurity towards the X‐point region. As a result, the impurity radiation is more intense near the X‐point than in the vicinity of the O‐point. This leads to the predominant cooling of the region around the X‐point. These results are in agreement with experimental observation with RMP application in the large helical device (LHD). The time scale of the thermal condensation instability is found to be of the order of 10 ms.

Fundamental limits from chaos on instability time predictions in compact planetary systems

ABSTRACT Instabilities in compact planetary systems are generically driven by chaotic dynamics. This implies that an instability time measured through direct N-body integration is not exact, but rather represents a single draw from a distribution of equally valid chaotic trajectories. In order to characterize the ‘errors’ on reported instability times from direct N-body integrations, we investigate the shape and parameters of the instability time distributions (ITDs) for ensembles of shadow trajectories that are initially perturbed from one another near machine precision. We find that in the limit where instability times are long compared to the Lyapunov (chaotic) time-scale, ITDs approach remarkably similar lognormal distributions with standard deviations ≈0.43 ± 0.16 dex, despite the instability times varying across our sample from 104 to 108 orbits. We find excellent agreement between these predictions, derived from ≈450 closely packed configurations of three planets, and a much wider validation set of $\approx 10\, 000$ integrations, as well as on $\approx 20\, 000$ previously published integrations of tightly packed five-planet systems, and a seven-planet resonant chain based on TRAPPIST-1, despite their instability time-scales extending beyond our analysed time-scale. We also test the boundary of applicability of our results on dynamically excited versions of our Solar system. These distributions define the fundamental limit imposed by chaos on the predictability of instability times in such planetary systems. It provides a quantitative estimate of the instrinsic error on an N-body instability time imprinted by chaos, approximately a factor of 3 in either direction.

The influence of inclinations on the dynamical stability of multi-planet systems

ABSTRACT A type of compactly spaced and comparably sized multi-exoplanet system similar to TRAPPIST-1 has been discovered recently. The stability of these systems is an important issue, requiring further study. We examined how the initial inclinations influence the stability of multi-planet systems and derived an empirical formula describing the dependence of the instability time-scale on planetary mass, space separation and initial inclination. We find the following. (i) If space separations between planets are greater than 12RH (mutual Hill radius), coplanar multi-planet systems with 10−6 ≤ μ ≤ 10−3 (reduced planetary mass μ = m/M*) will remain stable within 1010Tin (the innermost orbital period). (ii) If initial inclinations of planets are smaller than 10° and space separations are greater than 10RH, multi-planet systems consisting of ≥5 planets with μ ≥ 10−5 will remain stable within 1010Tin. (iii) Initial inclinations in [0°, 10°] have inconsequential effects on the instability time-scales of massive multi-planet systems (μ ≥ 10−5), because eccentricities (excited during evolution) dominate the stability of these systems. (iv) If the initial inclinations are large enough (≥10°), sharp increases of instability time-scales in groups with 10−3 ≥ μ ≥ 10−5 will be moderated. This article presents a comprehensive study of the influence of inclination on the stability of multi-planet systems and discusses critical space separations for a multi-planet system becoming unstable.

Gravitational-wave-driven tidal secular instability in neutron star binaries

We report the existence of a gravitational-wave-driven secular instability in neutron star binaries, acting on the equilibrium tide. The instability is similar to the classic Chandrasekhar-Friedman-Schutz instability of normal modes and is active when the spin of the primary star exceeds the orbital frequency of the companion. Modeling the neutron star as a Newtonian $n=1$ polytrope, we calculate the instability timescale, which can be as low as a few seconds at small orbital separations but still larger than the inspiral timescale. The implications for orbital and spin evolution are also briefly explored, where it is found that the instability slows down the inspiral and decreases the stellar spin.

Formation, gravitational clustering, and interactions of nonrelativistic solitons in an expanding universe

We investigate the formation, gravitational clustering, and interactions of solitons in a self-interacting, nonrelativistic scalar field in an expanding universe. Rapid formation of a large number of solitons is driven by attractive self-interactions of the field, whereas the slower clustering of solitons is driven by gravitational forces. Driven closer together by gravity, we see a rich plethora of dynamics in the soliton ``gas'' including mergers, scatterings, and formation of soliton binaries. The numerical simulations are complemented by analytic calculations and estimates of (i) the relevant instability length scales and timescales, (ii) individual soliton profiles and their stability, (iii) number density of produced solitons, and (iv) the two-point correlation function of soliton positions as evidence for gravitational clustering.

Scaling of instability timescales of Antarctic outlet glaciers based on one-dimensional similitude analysis

Abstract. Recent observations and ice-dynamic modeling suggest that a marine ice-sheet instability (MISI) might have been triggered in West Antarctica. The corresponding outlet glaciers, Pine Island Glacier (PIG) and Thwaites Glacier (TG), showed significant retreat during at least the last 2 decades. While other regions in Antarctica have the topographic predisposition for the same kind of instability, it is so far unclear how fast these instabilities would unfold if they were initiated. Here we employ the concept of similitude to estimate the characteristic timescales of several potentially MISI-prone outlet glaciers around the Antarctic coast. Our results suggest that TG and PIG have the fastest response time of all investigated outlets, with TG responding about 1.25 to 2 times as fast as PIG, while other outlets around Antarctica would be up to 10 times slower if destabilized. These results have to be viewed in light of the strong assumptions made in their derivation. These include the absence of ice-shelf buttressing, the one-dimensionality of the approach and the uncertainty of the available data. We argue however that the current topographic situation and the physical conditions of the MISI-prone outlet glaciers carry the information of their respective timescale and that this information can be partially extracted through a similitude analysis.

Revaluation of geomagnetic excursions recorded in lava flows from the Ceboruco and Tequila volcanic fields, trans-mexican volcanic belt

Detailed records of the Earth's magnetic field have shown that it has occasionally reversed its polarity. Several cases have also been found when the Earth Magnetic Field has significantly deviated for a relatively short time from its usual position defining a geomagnetic excursion, a kind of aborted reversal. Although many transitional paleodirections were revealed during the last decade in Central Mexico, their reliability was questioned. Recent paleomagnetic studies along the Trans-Mexican Volcanic Belt report contradictory results on the evidence of intermediary geomagnetic regimes. This work provides new paleomagnetic data which, combined with the information already reported, evaluate the fidelity of such events registered in the lava flows associated to the Tequila and Ceboruco Volcanic Fields. This critical reassessment allowed to discard the evidence of the Levantine geomagnetic excursion (362 ± 13 kA) but strongly confirms the occurrence of the Big Lost event (592 ± 20 ka). These findings represent an important contribution to the geomagnetic instability time scale for the last 1 Ma.

Ergoregion instability of exotic compact objects: Electromagnetic and gravitational perturbations and the role of absorption

Spinning horizonless compact objects may be unstable against an 'ergoregion instability'. We investigate this mechanism for electromagnetic perturbations of ultracompact Kerr-like objects with a reflecting surface, extending previous (numerical and analytical) work limited to the scalar case. We derive an analytical result for the frequency and the instability time scale of unstable modes which is valid at small frequencies. We argue that our analysis can be directly extended to gravitational perturbations of exotic compact objects in the black-hole limit. The instability for electromagnetic and gravitational perturbations is generically stronger than in the scalar case and it requires larger absorption to be quenched. We argue that exotic compact objects with spin $\chi\lesssim 0.7$ ($\chi\lesssim 0.9$) should have an absorption coefficient of at least $0.3\%$ ($6\%$) to remain linearly stable, and that an absorption coefficient of at least $\approx60\%$ would quench the instability for any spin. We also show that - in the static limit - the scalar, electromagnetic, and gravitatonal perturbations of the Kerr metric are related to one another through Darboux transformations.

Gravitationally produced top quarks and the stability of the electroweak vacuum during inflation

In the standard model the (Brout-Englert-)Higgs quartic coupling becomes negative at high energies rendering our current electroweak vacuum metastable, but with an instability timescale much longer than the age of the Current Universe. During cosmological Inflation, unless there is a non-minimal coupling to gravity, the Higgs field is pushed away from the origin of its potential due to quantum fluctuations. It is therefore a mystery how we have remained in our current vacuum if we went through such a period of Inflation. In this work we study the effect of top quarks created gravitationally during Inflation and their effect upon the Higgs potential using only General Relativity with minimal couplings and Standard Model particle physics. We show how the evolution of the Higgs field during Inflation is modified coming to the conclusion that this effect is non negligible for scales of Inflation close to or larger than the stability scale but small for scales where the Higgs is stable. Also, we briefly discuss the effect of other fermions to the Higgs instability.

Dynamical instability and its implications for planetary system architecture

We examine the effects that dynamical instability has on shaping the orbital properties of exoplanetary systems. Using N-body simulations of non-EMS (Equal Mutual Separation), multi-planet systems we find that the lower limit of the instability timescale $t$ is determined by the minimal mutual separation $K_{\rm min}$ in units of the mutual Hill radius. Planetary systems showing instability generally include planet pairs with period ratio $<1.33$. Our final period ratio distribution of all adjacent planet pairs shows dip-peak structures near first-order mean motion resonances similar to those observed in the \kepler\ planetary data. Then we compare the probability density function (PDF) of the de-biased \kepler\ period ratios with those in our simulations and find a lack of planet pairs with period ratio $> 2.1$ in the observations---possibly caused either by inward migration before the dissipation of the disk or by planet pairs not forming with period ratios $> 2.1$ with the same frequency they do with smaller period ratios. By comparing the PDF of the period ratio between simulation and observation, we obtain an upper limit of 0.03 on the scale parameter of the Rayleigh distributed eccentricities when the gas disk dissipated. Finally, our results suggest that a viable definition for a `packed' or `compact' planetary system be one that has at least one planet pair with a period ratio less than 1.33. This criterion would imply that 4\% of the \kepler\ systems (or 6\% of the systems with more than two planets) are compact.