Stellar Stability Research Articles

Visible and near-infrared spectro-interferometric analysis of the edge-on Be star o Aquarii

Aims. We present a detailed visible and near-infrared spectro-interferometric analysis of the Be-shell star o Aquarii from quasi-contemporaneous CHARA/VEGA and VLTI/AMBER observations. Methods. We analyzed spectro-interferometric data in the Hα (VEGA) and Brγ (AMBER) lines using models of increasing complexity: simple geometric models, kinematic models, and radiative transfer models computed with the 3D non-LTE code HDUST. Results. We measured the stellar radius of o Aquarii in the visible with a precision of 8%: 4.0 ± 0.3 R⊙. We constrained the circumstellar disk geometry and kinematics using a kinematic model and a MCMC fitting procedure. The emitting disk sizes in the Hα and Brγ lines were found to be similar, at ~10–12 stellar diameters, which is uncommon since most results for Be stars indicate a larger extension in Hα than in Brγ. We found that the inclination angle i derived from Hα is significantly lower (~15°) than the one derived from Brγ: i ~ 61.2° and 75.9°, respectively. While the two lines originate from a similar region of the disk, the disk kinematics were found to be near to the Keplerian rotation (i.e., β = −0.5) in Brγ (β ~ −0.43), but not in Hα (β ~ −0.30). After analyzing all our data using a grid of HDUST models (BeAtlas), we found a common physical description for the circumstellar disk in both lines: a base disk surface density Σ0 = 0.12 g cm−2 and a radial density law exponent m = 3.0. The same kind of discrepancy, as with the kinematic model, is found in the determination of i using the BeAtlas grid. The stellar rotational rate was found to be very close (~96%) to the critical value. Despite being derived purely from the fit to interferometric data, our best-fit HDUST model provides a very reasonable match to non-interferometric observables of o Aquarii: the observed spectral energy distribution, Hα and Brγ line profiles, and polarimetric quantities. Finally, our analysis of multi-epoch Hα profiles and imaging polarimetry indicates that the disk structure has been (globally) stable for at least 20 yr. Conclusions. Looking at the visible continuum and Brγ emission line only, o Aquarii fits in the global scheme of Be stars and their circumstellar disk: a (nearly) Keplerian rotating disk well described by the viscous decretion disk (VDD) model. However, the data in the Hα line shows a substantially different picture that cannot fully be understood using the current generation of physical models of Be star disks. The Be star o Aquarii presents a stable disk (close to the steady-state), but, as in previous analyses, the measured m is lower than the standard value in the VDD model for the steady-state regime (m = 3.5). This suggests that some assumptions of this model should be reconsidered. Also, such long-term disk stability could be understood in terms of the high rotational rate that we measured for this star, the rate being a main source for the mass injection in the disk. Our results on the stellar rotation and disk stability are consistent with results in the literature showing that late-type Be stars are more likely to be fast rotators and have stable disks.

Estimates dark halo parameters in S-galaxies

The dark mass problem is the most important for cosmology and galaxies physics. Various observational data of galaxies and galaxies clusters kinematics and dynamics require presence of massive dark matter. We estimate the dark mass within the galaxies optical radius using several different approaches, such as the maximum disk model, the marginal condition of the stellar disk gravitational stability and the vertical equilibrium condition in the galactic disk. The distribution functions of the relative dark mass within the optical radius Ropt for a set of 50 galaxies are constructed. Most of the objects from our set have a relative mass within µ = 2. This agrees well with the results of numerical simulations.

The regular dynamics through the finite‐time Lyapunov exponent distributions in 3D Hamiltonian systems

AbstractWe investigate the application as a technique of the so‐called finite‐time Lyapunov exponent, a scalar value that measures the average, or integrated, separation between trajectories in integrable dynamical systems to quantify the predictability limit of the asymptotic global behavior of old compact star systems (1–10 Gyr), for instance, neutron stars. For this purpose, the Hamiltonian systems with a three‐dimensional self‐gravitating axisymmetric potential are superimposed due to the influence of different birth and kick velocity distributions. We find the behavior of the density distributions P(x) for the finite‐time exponents, which follow a log‐normal distribution (transformed into a Gaussian distribution), with a given mean deviation centered around the global values, at larger Δt. It is shown that simple models of distributions reflect the underlying dynamics. We also analyze the predictability and the deviation vector ω(t), obtained from the distributions, by randomly selecting the initial deviation directions, and consequently the stellar dynamic stability of the periodic orbits, in three‐dimensional (3D) Hamiltonian systems over time. The behavior of the orbits is strongly influenced by the regular nature of the motion.

A new generalised solution to generate anisotropic compact star models in the Karmarkar space-time manifold

In the present article a new generalised solution is obtained for anisotropic matter configuration using Karmarkar’s condition. The solution is used to model the interior structure of anisotropic relativistic objects as it satisfies all necessary physical conditions. The pressure, density and metric potentials are free from any singularities and exhibit well behaved nature inside the anisotropic fluid sphere. The TOV equation is well maintained within the stellar configuration and all energy conditions hold good. The causality condition is well satisfied for our stellar models and stability of compact star models is further verified via Herrera’s cracking method. Harrison-Zeldovich-Novikov criterion for stability is also satisfied by our model. The adiabatic index is greater than $\frac{4}{3}$ throughout the stellar interior and the compactification factor also lies within the Buchdahl limit i.e. $M/R \le 4/9$ . We investigate the models for two compact stars PSRJ0348+0432 and SAX J1808.4-3658 within the framework of the general theory of relativity. The estimated mass and radius are in close agreement with the observational data. we extensively study the solutions corresponding to compact star PSRJ0348+0432 for $ n = 0, 1, 2, 3, 4, 4.5$ and the detailed graphical analysis is provided to substantiate the viability of the compact star model. One specific feature of our solution is that for large values of n, i.e. for $ n > 5$ solution reduces to Finch and Skea type solution.

High-β equilibrium and ballooning stability of the low aspect ratio CNT stellarator

The existence and ballooning-stability of low aspect ratio stellarator equilibria is predicted for the Columbia Neutral Torus (CNT) with the aid of 3D numerical tools. In addition to having a low aspect ratio, CNT is characterized by a low magnetic field and small plasma volume. Also, highly overdense plasmas were recently heated in CNT by means of microwaves. These characteristics suggest that CNT might attain relatively high values of plasma beta and thus be of use in the experimental study of stellarator stability to high-beta instabilities such as ballooning modes. As a first step in that direction, here the ballooning stability limit is found numerically. Depending on the particular magnetic configuration we expect volume-averaged β limits in the range 0.9%–3.0%, and possibly higher, and observe indications of a second region of ballooning stability. As the aspect ratio is reduced, stability is found to increase in some configurations and decrease in others. Energy-balance estimates using stellarator scaling laws indicate that the lower β limit may be attainable with overdense heating at powers of 40 to 100 kW. The present study serves the additional purpose of testing VMEC and other stellarator codes at high values of β and at low aspect ratios. For this reason, the study was carried out both for free boundary, for maximum fidelity to experiment, as well as with a fixed boundary, as a numerical test.

On the effect of turbulent anisotropy on pulsation stability of stars

Within the framework of a non-local time-dependent stellar convection theory, we study in detail the effect of turbulent anisotropy on stellar pulsation stability. The results show that anisotropy has no substantial influence on pulsation stability of g modes and low-order (radial order nr < 5) p modes. The effect of turbulent anisotropy increases as the radial order increases. When turbulent anisotropy is neglected, most high-order (nr > 5) p modes of all low-temperature stars become unstable. Fortunately, within a wide range of the anisotropic parameter c3, stellar pulsation stability is not sensitive to the specific value of c3. Therefore it is safe to say that calibration errors of the convective parameter c3 do not cause any uncertainty in the calculation of stellar pulsation stability.

Spiral eigenmodes triggered by grooves in the phase space of disc galaxies

We use linear perturbation theory to investigate how a groove in the phase space of a disc galaxy changes the stellar disc's stability properties. Such a groove is a narrow trough around a fixed angular momentum from which most stars have been removed, rendering part of the disc unresponsive to spiral waves. We find that a groove can dramatically alter a disc's eigenmode spectrum by giving rise to a set of vigorously growing eigenmodes. These eigenmodes are particular to the grooved disc and are absent from the original ungrooved disc's mode spectrum. We discuss the properties and possible origin of the different families of new modes. By the very nature of our technique, we prove that a narrow phase-space groove can be a source of rapidly growing spiral patterns that are true eigenmodes of the grooved disc and that no non-linear processes need to be invoked to explain their presence in N-body simulations of disc galaxies. Our results lend support to the idea that spiral structure can be a recurrent phenomenon, in which one generation of spiral modes alters a disc galaxy's phase space in such a way that a following generation of modes is destabilized.

Stellar stability in brane-worlds revisited

We consider here the general conditions for the stability of brane stars that obey a so called a minimal setup: the nonlocal anisotropic stress and energy flux are absent everywhere, and the only permitted Weyl correction is the interior solution of the nonlocal energy density. Along with a series of simple conditions, we show that the Germani–Maartens solution with a constant density sets up the upper bound for the compactness of that particular class of brane stars. The general demonstration is based upon the properties of the interior solutions of the stars, although we also show that the minimal setup implies a Schwarzschild exterior.

Stellar Stability in the Braneworld

We study the properties of astrophysical systems in a Brane World scenario. In particular, the consequences of local terms that emerge from extra-dimensional gravity are explored through the modified Tolman-Oppenheimer-Volkoff equation. We compute the induced changes into mass, density and compactness of objects like white dwarfs and neutron stars. The main corrections in comparison with the known results of General Relativity are given in terms of the ratio ρ0/λ, where ρ0 is the central energy density of the stellar distribution and λ is the brane tension. As a result of these modifications, We obtain that the compactness of both, neutron stars and white dwarf decreases with respect to the value of General Relativity.

Radial oscillations and stability of compact stars in Eddington-inspired Born-Infeld gravity

We study the hydrostatic equilibrium structure of compact stars in the Eddington-inspired Born-Infeld gravity recently proposed by Ba\~nados and Ferreira [Phys. Rev. Lett. 105, 011101 (2010)]. We also develop a framework to study the radial perturbations and stability of compact stars in this theory. We find that the standard results of stellar stability still hold in this theory. The frequency square of the fundamental oscillation mode vanishes for the maximum-mass stellar configuration. The dependence of the oscillation mode frequencies on the coupling parameter $\ensuremath{\kappa}$ of the theory is also investigated. We find that the fundamental mode is insensitive to the value of $\ensuremath{\kappa}$, while higher-order modes depend more strongly on $\ensuremath{\kappa}$.

Theoretical seismic properties of pre-main sequenceγ Doradus pulsators

Context. gamma Doradus (gamma Dor) are late A and F-type stars pulsating with high order gravity modes (g-modes). The existence of different evolutionary phases crossing the gamma Dor instability strip raises the question of the existence of pre-main sequence (PMS) gamma Dor stars. Aims. We intend to study the differences between the asteroseismic behaviour of PMS and main sequence (MS) gamma Dor pulsators as it is predicted by the current theory of stellar evolution and stability. Methods. We explore the adiabatic and non-adiabatic properties of high order g-modes in a grid of PMS and MS models covering the mass range 1.2 Msun < Mstar < 2.5 Msun. Results. We derive the theoretical instability strip (IS) for the PMS gamma Dor pulsators. This IS covers the same effective temperature range as the MS gamma Dor one. Nevertheless, the frequency domain of unstable modes in PMS models with a fully radiative core is larger than in MS models, even if they present the same number of unstable modes. Moreover, the differences between MS and PMS internal structures are reflected on the average values of the period spacing as well as on the dependence of the period spacing on the radial order of the modes, opening the window to the determination of the evolutionary phase of gamma Dor stars from their pulsation spectra.

Determining the long living quasi-normal modes of relativistic stars

Methods of finding quasi-normal modes of non-rotating relativistic stars have been well established, however, none of the existing treatments which take spacetime and fluid oscillations fully into account can determine modes of long decay time, e.g., the p and g mode series, or the f modes for stars with low compactness ratio (M/R). In this paper we show how the quasi-normal modes of long lifetime can be determined through refinements of a treatment originally due to Detweiler and Lindblom. The determination of the p mode series has been argued in the literature to have implication on the life time of gravitational wave sources and stellar stability. In this paper we 1) provide detailed steps in our treatment to facilitate future effort in this direction; 2) correct mistakes in the literature on the formulation; and 3) analyse the accuracy of the quasi-normal mode frequencies obtained and the limitations of the treatment.

The DEMO Quasisymmetric Stellarator

The NSTAB nonlinear stability code solves differential equations in conservation form, and the TRAN Monte Carlo test particle code tracks guiding center orbits in a fixed background, to provide simulations of equilibrium, stability, and transport in tokamaks and stellarators. These codes are well correlated with experimental observations and have been validated by convergence studies. Bifurcated 3D solutions of the 2D tokamak problem have been calculated that model persistent disruptions, neoclassical tearing modes (NTMs) and edge localized modes (ELMs) occurring in the International Thermonuclear Experimental Reactor (ITER), which does not pass the NSTAB simulation test for nonlinear stability. So we have designed a quasiaxially symmetric (QAS) stellarator with similar proportions as a candidate for the demonstration (DEMO) fusion reactor that does pass the test [1]. The configuration has two field periods and an exceptionally accurate 2D symmetry that furnishes excellent thermal confinement and good control of the prompt loss of alpha particles. Robust coils are found from a filtered form of the Biot-Savart law based on a distribution of current over a control surface for the coils and the current in the plasma defined by the equilibrium calculation. Computational science has addressed the issues of equilibrium, stability, and transport, so it remains to develop an effective plan to construct the coils and build a diverter.

THE FREQUENCY OF LOW-MASS EXOPLANETS

We report first results from the Anglo-Australian Telescope Rocky Planet Search - an intensive, high-precision Doppler planet search targeting low-mass exoplanets in contiguous 48 night observing blocks. On this run we targeted 24 bright, nearby and intrinsically stable Sun-like stars selected from the Anglo-Australian Planet Search's main sample. These observations have already detected one low-mass planet reported elsewhere (HD16417b), and here we reconfirm the detection of HD4308b. Further, we have Monte-Carlo simulated the data from this run on a star-by-star basis to produce robust detection constraints. These simulations demonstrate clear differences in the exoplanet detectability functions from star to star due to differences in sampling, data quality and intrinsic stellar stability. They reinforce the importance of star-by-star simulation when interpreting the data from Doppler planet searches. The simulations indicate that for some of our target stars we are sensitive to close-orbiting planets as small as a few Earth masses. The two low-mass planets present in our 24 star sample indicate that the exoplanet minimum mass function at low masses is likely to be a flat alpha ~ -1 (for dN/dM proportional to M^alpha) and that between 15+/-10% (at alpha=-0.3) and 48+/-34% (at alpha=-1.3) of stars host planets with orbital periods of less than 16 days and minimum masses greater than 3 Mearth.

SPECTOR3D: a resistive magnetohydrodynamic stability code for stellarators

SPECTOR3D is a magnetohydrodynamic (MHD) code designed to study the resistive stability and mode spectrum of stellarators. It finds the spectrum of the linearized, compressible, resistive MHD equations. Some typical results are given for a tokamak model with toroidal field ripple and a 17-period Heliotron.

Generalized Analytic Stellar Stability Criteria with Applications to Luminous Stellar Envelopes

Baker's one-zone model of a radiative stellar envelope is generalized here to include additional forces that can be represented as a function of only the stellar radius. The criteria for dynamical, secular, and pulsational stability against radial perturbations are derived and expressed in simple, general analytic forms. Applications are made to the outer envelopes of luminous blue variables (LBVs). The acceleration of stellar-wind mass loss has no effect on the stability criteria, but axial rotation and slowly adapting convective turbulence produce more complicated effects, depending on whether the envelope is dynamically stable or not. On the other hand, rotation and turbulence are probably very weak in most LBV outer envelopes.

Stellarator stability with respect to global kinetic ballooning modes

Ballooning modes are usually the most dangerous ideal MHD instabilities in stellarators, but the unstable ballooning modes often have such short perpendicular wavelengths that finite Larmor radius effects are sufficient to stabilize the plasma. We use semiclassical techniques to analyse this effect. In tokamaks the ignorable toroidal coordinate leads to a simple quantization of the ballooning mode, but this is not the case for stellarators. The ballooning mode dynamics in a stellarator model may possess a separation of timescales, in which case the system is integrable and quantization is straightforward, but we also present a method for determining marginal stability which is applicable to the non-integrable case.

Stellar Stability by Thermodynamic Instability

For gravity-dominated systems the three features shrinking <=> energy decrease <=> temperature increase are dynamically linked together. So are their inverses: expansion <=> energy increase <=> temperature decrease. We exhibit these features by one classical particle in a suitable environment, and by many particles with purely attractive interactions. We then show how the ensuing negative heat capacity tames an explosive energy input.

Influence of magnetic topology on transport and stability in stellarators

The influence of the magnetic topology on transport and stability has been investigated in four stellarators: an almost shearless medium size flexible heliac (TJ-II), a medium size and a large heliotron (CHS and LHD) with shear, and a quasihelically symmetric device (HSX) with moderate shear. All of these have variable rotational transform profiles and magnetic ripples. Using these capabilities, bifurcated states can appear and plasma can jump from one to another with subsequent changes in the transport properties. Low rational values of ι/2π can create transport barriers in LHD and TJ-II when they are located close to the plasma core or at the edge. The key ingredient for transport barriers is a positive and sheared electric field. Internal transport barriers also appear in CHS, but the role of rationals is not clear yet in this device. The time evolution of the electric field shows the onset of a bifurcation triggered either by the rational or by the presence of the ion and electron roots. The electric potential inside ITBs follows the ECE-temperature profile in a fast time scale. The plasma stability properties and its effect on the viscosity are also studied in the HSX, and the influence of the dynamics of rational surface is studied in the LHD and TJ-II stellarators.

Reactors with Stellarator Stability and Tokamak Transport

The discovery of quasiaxially symmetric stellarators whose magnetic spectrum has approximate two-dimensional symmetry opens up the possibility of designing fusion reactors that have tokamak transport and stellarator stability. Prototypes with two or three field periods have asymmetries almost as small as the coefficients for a typical tokamak that are associated with ripple from the toroidal coils or helical excursion of the magnetic axis resulting from instability. We have found modular coils that are only moderately twisted and produce robust flux surfaces that do not deteriorate when changes are made in the magnetic field. This work is bolstered by recent stellarator experiments that have exceeded stability limits predicted by linear theory. The problem may be that force balance and stability are lost across islands if the equilibrium equations are not in conservation form.