Secular Instability Research Articles

TWO-COMPONENT SECULAR GRAVITATIONAL INSTABILITY IN A PROTOPLANETARY DISK: A POSSIBLE MECHANISM FOR CREATING RING-LIKE STRUCTURES

The instability in protoplanetary disks due to gas-dust friction and self-gravity of gas and dust is investigated by linear analysis. In the case where the dust to gas ratio is enhanced and turbulence is week, the instability grows, even in gravitationally stable disks, on a timescale of order $10^{4- 5}$yr at a radius of order 100AU. If we ignore the dynamical feedback from dust grains in the gas equation of motion, the instability reduces to the so-called "secular gravitational instability", which was investigated previously as an instability of dust in a fixed background gas flow. In this work, we solve the equations of motion for both gas and dust consistently and find that long-wavelength perturbations are stable, in contrast to the secular gravitational instability in the simplified treatment. This may indicate that we should not neglect small terms in equation of motion if the growth rate is small. The instability is expected to form ring structures in protoplanetary disks. The width of the ring formed at a radius of 100 AU is a few tens of AU. Therefore, the instability is a candidate for the formation mechanism of observed ring-like structures in disks. Another aspect of the instability is the accumulation of dust grains, and hence the instability may play an important role in the formation of planetesimals, rocky protoplanets, and cores of gas giants located at radii $\sim$100 AU. If these objects survive the dispersal of the gaseous component of the disk, they may be the origin of debris disks.

On radial anisotropy limits in stellar systems

Following earlier authors we re-examine the upper limits on the radial velocity anisotropy of general stellar systems; these constraints coming generically from phase-space density positivity, stability, and separability. Galaxy models almost always satisfy an inequality β < γ/2, i.e. the radial anisotropy is locally no greater than half of the logarithmic density slope. Some complex separable models are the only known cases which disobey this inequality and do so by having an exceptionally large anisotropy at the centre. Here we present new families of non-separable but simple models which have β > γ/2. Such large, superthreshold anisotropy always occurs in a finite region in between an isotropic core and an isotropic outer boundary. Our models are always self-consistent and hence maintain the positivity of the phase-space density. Nevertheless, regions with superthreshold anisotropy are potentially subject to secular instability and may thus be observed in a short-lived phase of galaxies.

THE INFLUENCE OF THERMAL PRESSURE ON EQUILIBRIUM MODELS OF HYPERMASSIVE NEUTRON STAR MERGER REMNANTS

The merger of two neutron stars leaves behind a rapidly spinning hypermassive object whose survival is believed to depend on the maximum mass supported by the nuclear equation of state, angular momentum redistribution by (magneto-)rotational instabilities, and spindown by gravitational waves. The high temperatures (~5-40 MeV) prevailing in the merger remnant may provide thermal pressure support that could increase its maximum mass and, thus, its life on a neutrino-cooling timescale. We investigate the role of thermal pressure support in hypermassive merger remnants by computing sequences of spherically-symmetric and axisymmetric uniformly and differentially rotating equilibrium solutions to the general-relativistic stellar structure equations. Using a set of finite-temperature nuclear equations of state, we find that hot maximum-mass critically spinning configurations generally do not support larger baryonic masses than their cold counterparts. However, subcritically spinning configurations with mean density of less than a few times nuclear saturation density yield a significantly thermally enhanced mass. Even without decreasing the maximum mass, cooling and other forms of energy loss can drive the remnant to an unstable state. We infer secular instability by identifying approximate energy turning points in equilibrium sequences of constant baryonic mass parametrized by maximum density. Energy loss carries the remnant along the direction of decreasing gravitational mass and higher density until instability triggers collapse. Since configurations with more thermal pressure support are less compact and thus begin their evolution at a lower maximum density, they remain stable for longer periods after merger.

What controls star formation in the central 500 pc of the Galaxy?

The star formation rate (SFR) in the Central Molecular Zone (CMZ, i.e. the central 500 pc) of the Milky Way is lower by a factor of >10 than expected for the substantial amount of dense gas it contains, which challenges current star formation theories. In this paper, we quantify which physical mechanisms could be responsible. On scales larger than the disc scale height, the low SFR is found to be consistent with episodic star formation due to secular instabilities or possibly variations of the gas inflow along the Galactic bar. The CMZ is marginally Toomre-stable when including gas and stars, but highly Toomre-stable when only accounting for the gas, indicating a low condensation rate of self-gravitating clouds. On small scales, we find that the SFR in the CMZ may be caused by an elevated critical density for star formation due to the high turbulent pressure. The existence of a universal density threshold for star formation is ruled out. The HI-H$_2$ phase transition of hydrogen, the tidal field, a possible underproduction of massive stars due to a bottom-heavy initial mass function, magnetic fields, and cosmic ray or radiation pressure feedback also cannot individually explain the low SFR. We propose a self-consistent cycle of star formation in the CMZ, in which the effects of several different processes combine to inhibit star formation. The rate-limiting factor is the slow evolution of the gas towards collapse - once star formation is initiated it proceeds at a normal rate. The ubiquity of star formation inhibitors suggests that a lowered central SFR should be a common phenomenon in other galaxies. We discuss the implications for galactic-scale star formation and supermassive black hole growth, and relate our results to the star formation conditions in other extreme environments.

Uniformly rotating neutron stars in the global and local charge neutrality cases

In our previous treatment of neutron stars, we have developed the model fulfilling global and not local charge neutrality. In order to implement such a model, we have shown the essential role by the Thomas–Fermi equations, duly generalized to the case of electromagnetic field equations in a general relativistic framework, forming a coupled system of equations that we have denominated Einstein–Maxwell–Thomas–Fermi (EMTF) equations. From the microphysical point of view, the weak interactions are accounted for by requesting the β stability of the system, and the strong interactions by using the σ – ω – ρ nuclear model, where σ , ω and ρ are the mediator massive vector mesons. Here we examine the equilibrium configurations of slowly rotating neutron stars by using the Hartle formalism in the case of the EMTF equations indicated above. We integrate these equations of equilibrium for different central densities ρ c and circular angular velocities Ω and compute the mass M , polar R p and equatorial R e q radii, angular momentum J , eccentricity ϵ , moment of inertia I , as well as quadrupole moment Q of the configurations. Both the Keplerian mass-shedding limit and the axisymmetric secular instability are used to construct the new mass–radius relation. We compute the maximum and minimum masses and rotation frequencies of neutron stars. We compare and contrast all the results for the global and local charge neutrality cases.

ON THE MAXIMUM MASS AND MINIMUM ROTATION PERIOD OF RELATIVISTIC UNIFORMLY ROTATING WHITE DWARFS

We investigate the stability of general relativistic uniformly rotating white dwarfs against secular and dynamical instabilities. We determine the minimum rotation period of stable white dwarfs depending on chemical composition of the white dwarf matter taking into account the Coulomb interactions as well as the nuclear interactions and the electroweak equilibrium at high densities, within the relativistic Feynman-Metropolis-Teller equation of state.

The growth of galactic bulges through mergers in Λ CDM haloes revisited – I. Present-day properties

We use the Millennium I and II cosmological simulations to revisit the impact of mergers in the growth of bulges in central galaxies in the LCDM scenario. We seed galaxies within the growing CDM haloes using semi-empirical relations to assign stellar and gaseous masses, and an analytic treatment to estimate the transfer of stellar mass to the bulge of the remnant after a galaxy merger. We find that this model roughly reproduces the observed correlation between the bulge-to-total (B/T) mass ratio and stellar mass in present-day central galaxies as well as their observed demographics, although low-mass B/T<0.1 (bulgeless) galaxies might be scarce relative to the observed abundance. In our merger-driven scenario, bulges have a composite population made of (i) stars acquired from infalling satellites, (ii) stars transferred from the primary disc due to merger-induced perturbations, and (iii) newly formed stars in starbursts triggered by mergers. We find that (i) and (ii) are the main channels of mass assembly, with the first being dominant for massive galaxies, creating large bulges with different stellar populations than those of the inner discs, while the second is dominant for intermediate/low-mass galaxies creating small bulges with similar stellar populations to the inner discs. We associate the dominion of the first (second) channel to classical (pseudo) bulges, and compare the predicted fractions to observations. We remark that our treatment does not include other mechanisms of bulge growth such as intrinsic secular disc instabilities or misaligned gas accretion. We find that the evolution of the stellar and gaseous contents of the satellite as it moves towards the central galaxy is a key ingredient in setting the morphology of the remnant, and that a good match to the observed bulge demographics occurs when this evolution proceeds closely to that of the central galaxy.

PLANETESIMAL FORMATION IN MAGNETOROTATIONALLY DEAD ZONES: CRITICAL DEPENDENCE ON THE NET VERTICAL MAGNETIC FLUX

Turbulence driven by magnetorotational instability (MRI) affects planetesimal formation by inducing diffusion and collisional fragmentation of dust particles. We examine conditions preferred for planetesimal formation in MRI-inactive "dead zones" using an analytic dead-zone model based on our recent resistive MHD simulations. We argue that successful planetesimal formation requires not only a sufficiently large dead zone (which can be produced by tiny dust grains) but also a sufficiently small net vertical magnetic flux (NVF). Although often ignored, the latter condition is indeed important since the NVF strength determines the saturation level of turbulence in MRI-active layers. We show that direct collisional formation of icy planetesimal across the fragmentation barrier is possible when the NVF strength is lower than 10 mG (for the minimum-mass solar nebula model). Formation of rocky planetesimals via the secular gravitational instability is also possible within a similar range of the NVF strength. Our results indicate that the fate of planet formation largely depends on how the NVF is radially transported in the initial disk formation and subsequent disk accretion processes.

Differentially-rotating neutron star models with a parametrized rotation profile

We analyze the impact of the choice rotation law on equilibrium sequences of relativistic differentially-rotating neutron stars in axisymmetry. The maximum allowed mass for each model is strongly affected by the distribution of angular velocity along the radial direction and by the consequent degree of differential rotation. In order to study the wide parameter space implied by the choice of rotation law, we introduce a functional form that generalizes the so called "j-const. law" adopted in all previous work. Using this new rotation law we reproduce the angular velocity profile of differentially-rotating remnants from the coalescence of binary neutron stars in various 3-dimensional dynamical simulations. We compute equilibrium sequences of differentially rotating stars with a polytropic equation of state starting from the spherically symmetric static case. By analyzing the sequences at constant ratio, T/|W|, of rotational kinetic energy to gravitational binding energy, we find that the parameters that best describe the binary neutron star remnants cannot produce equilibrium configurations with values of T/|W| that exceed 0.14, the criterion for the onset of the secular instability.

MINIMUM DUST ABUNDANCES FOR PLANETESIMAL FORMATION VIA SECULAR GRAVITATIONAL INSTABILITIES

We estimate minimum dust abundances required for secular gravitational instability (SGI) to operate at the midplane dust layer of protoplanetary disks. For SGI to be a viable process, the growth time of the instability T_grow must be shorter than the radial drift time of the dust T_drift. The growth time depends on the turbulent diffusion parameter alpha, because the modes with short wavelengths are stabilized by turbulent diffusion. Assuming that turbulence is excited via the Kelvin-Helmholtz or streaming instabilities in the dust layer, and that its strength is controlled by the energy supply rate from dust accretion, we estimate the diffusion parameter and the growth time of the instability. The condition T_grow < T_drift requires that the dust abundance must be greater than a critical abundance Z_min, which is a function of the Toomre parameter Q_g and aspect ratio h_g / r of the gas disk. For a wide range of parameter space, the required dust abundance is less than 0.1. A slight increase in dust abundance opens a possible route for the dust to directly collapse to planetesimals.

SECULAR GRAVITATIONAL INSTABILITY OF A DUST LAYER IN SHEAR TURBULENCE

We perform a linear stability analysis of a dust layer in a turbulent gas disk. Youdin (2011) investigated the secular gravitational instability of a dust layer using hydrodynamic equations with a turbulent diffusion term. We obtain essentially the same result independently of Youdin (2011). In the present analysis, we restrict the area of interest to small dust particles, while investigating the secular gravitational instability in a more rigorous manner. We discuss the time evolution of the dust surface density distribution using a stochastic model and derive the advection-diffusion equation. The validity of the analysis by Youdin (2011) is confirmed in the strong drag limit. We demonstrate quantitatively that the finite thickness of a dust layer weakens the secular gravitational instability and that the density-dependent diffusion coefficient changes the growth rate. We apply the obtained results to the turbulence driven by the shear instability and find that the secular gravitational instability is faster than the radial drift when the gas density is three times as large as that in the minimum-mass disk model. If the dust particles are larger than chondrules, the secular gravitational instability grows within the lifetime of a protoplanetary disk.

Equilibrium and stability of а thin torus in the gravitation field of a galaxy

Self-gravitating thin ring in the gravitation field of a galaxy is investigated. It's shown that all toroidal structures are subjected to the secular instability, but the dynamical instability is possible under some conditions. Self-gravitating formation can “diffuse” forming some ring system or brake up to separate self-gravitating condensations.

A SINGLE DEGENERATE PROGENITOR MODEL FOR TYPE Ia SUPERNOVAE HIGHLY EXCEEDING THE CHANDRASEKHAR MASS LIMIT

Recent observations of Type Ia supernovae (SNe Ia) suggest that some of the progenitor white dwarfs (WDs) had masses up to 2.4-2.8 M_sun, highly exceeding the Chandrasekhar mass limit. We present a new single degenerate (SD) model for SN Ia progenitors, in which the WD mass possibly reaches 2.3-2.7 M_sun. Three binary evolution processes are incorporated; optically thick winds from mass-accreting WDs, mass-stripping from the binary companion star by the WD winds, and WDs being supported by differential rotation. The WD mass can increase by accretion up to 2.3 (2.7) M_sun from the initial value of 1.1 (1.2) M_sun, being consistent with high luminosity SNe Ia such as SN 2003fg, SN 2006gz, SN 2007if, and SN 2009dc. There are three characteristic mass ranges of exploding WDs. In an extreme massive case, differentially rotating WDs explode as an SN Ia soon after the WD mass exceeds 2.4 M_sun because of a secular instability at T/|W|\sim 0.14. For a mid mass range of M_WD=1.5-2.4 M_sun, it takes some time (spinning-down time) until carbon is ignited to induce an SN Ia explosion after the WD mass has reached maximum, because it needs a loss or redistribution of angular momentum. For a lower mass case of rigidly rotating WDs, M_WD=1.38-1.5 M_sun, the spinning-down time depends on the timescale of angular momentum loss from the WD. The difference in the spinning-down time may produce the "prompt" and "tardy" components. We also suggest the very bright super-Chandrasekhar mass SNe Ia are born in a low metallicity environment.

Evolution of growing black holes in axisymmetric galaxy cores

NBody realizations of axisymmetric collisional galaxy cores (e.g. M32, M33, NGC205, Milky Way) with embedded growing black holes are presented. Stars which approach the disruption sphere are disrupted and accreted to the black hole. We measure the zone of influence of the black hole and disruption rates in relaxation time scales. We show that secular gravitational instabilities dominate the initial core dynamics, while the black hole is small and growing due to consumption of stars. Later, the black hole potential dominates the core, and loss cone theory can be applied. Our simulations show that central rotation in galaxies can not be neglected for relaxed systems, and compare and discuss our results with the standard theory of spherically symmetric systems.

A quasi-radial stability criterion for rotating relativistic stars

Abstract The stability properties of relativistic stars against gravitational collapse to black holes is a classical problem in general relativity. In 1988, a sufficient criterion for secular instability was established by Friedman, Ipser &amp; Sorkin, who proved that a sequence of uniformly rotating barotropic stars are secularly unstable on one side of a turning point and then argued that a stronger result should hold: that the sequence should be stable on the opposite side, with the turning point marking the onset of secular instability. We show here that this expectation is not met. By computing in full general relativity the F-mode frequency for a large number of rotating stars, we show that the neutral-stability point, that is, where the frequency becomes zero, differs from the turning point for rotating stars. Using numerical simulations, we validate that the new criterion can be used to assess the dynamical stability of relativistic rotating stars.

TWIN BINARIES: STUDIES OF STABILITY, MASS TRANSFER, AND COALESCENCE

Motivated by suggestions that binaries with almost equal-mass components ("twins") play an important role in the formation of double neutron stars and may be rather abundant among binaries, we study the stability of synchronized close and contact binaries with identical components in circular orbits. In particular, we investigate the dependency of the innermost stable circular orbit on the core mass, and we study the coalescence of the binary that occurs at smaller separations. For twin binaries composed of convective main-sequence stars, subgiants, or giants with low mass cores (M_c <~0.15M, where M is the mass of a component), a secular instability is reached during the contact phase, accompanied by a dynamical mass transfer instability at the same or at a slightly smaller orbital separation. Binaries that come inside this instability limit transfer mass gradually from one component to the other and then coalesce quickly as mass is lost through the outer Lagrangian points. For twin giant binaries with moderate to massive cores (M_c >~0.15M), we find that stable contact configurations exist at all separations down to the Roche limit, when mass shedding through the outer Lagrangian points triggers a coalescence of the envelopes and leaves the cores orbiting in a central tight binary. In addition to the formation of binary neutron stars, we also discuss the implications of our results for the production of planetary nebulae with double degenerate central binaries.

A Single Degenerate Model for Ultra Super-Chandrasekhar Mass Progenitors of Type Ia Supernovae – Young and Low Metallicity Environments –

AbstractSome Type Ia supernovae (SNe Ia) are suggested to have progenitor white dwarfs (WDs) with mass of up to 2.4–2.8 M⊙, highly exceeding the Chandrasekhar mass limit. We present a new single degenerate (SD) model for SNe Ia progenitors, in which the WD mass can increase by accretion up to 2.3 (2.7) M⊙ from the initial value of 1.1 (1.2) M⊙. The results are consistent with high luminosity SNe Ia such as SN 2003fg, SN 2006gz, SN 2007if, and SN 2009dc. There are three characteristic mass ranges of exploding WDs. In an extreme massive case, differentially rotating WDs explode as a SNe Ia soon after the WD mass exceeds 2.4 M⊙ because of a secular instability at T/|W|~0.14. For a mid mass range of MWD=1.5–2.4 M⊙, which is supported by differential rotation, it takes some spinning-down time until carbon is ignited to induce an SN Ia explosion. For a lower mass range of MWD=1.38–1.5 M⊙, they can be supported by rigid rotation until the angular momentum is lost. We also suggest the ultra super-Chandrasekhar mass SNe Ia are born in young and low metallicity environments.

STABILITY OF MRI-TURBULENT ACCRETION DISKS

Based on the characteristics of the magnetorotational instability (MRI) and the MRI-driven turbulence, we construct a steady model for a geometrically thin disk using "non-standard" $\alpha$-prescription. The efficiency of the angular momentum transport depends on the magnetic Prandtl number, $Pm = \nu/\eta$, where $\nu$ and $\eta$ are the microscopic viscous and magnetic diffusivities. In our disk model, Shakura-Sunyaev's $\alpha$-parameter has a power-law dependence on the magnetic Prandtl number, that is $\alpha \propto Pm^\delta$ where $\delta$ is the constant power-law index. Adopting Spitzer's microscopic diffusivities, the magnetic Prandtl number becomes a decreasing function of the disk radius when $\delta > 0$. The transport efficiency of the angular momentum and the viscous heating rate are thus smaller in the outer part of the disk, while these are impacted by the size of index $\delta$. We find that the disk becomes more unstable to the gravitational instability for a larger value of index $\delta$. The most remarkable feature of our disk model is that the thermal and secular instabilities can grow in its middle part even if the radiation pressure is negligibly small in the condition $\delta > 2/3$. In the realistic disk systems, it would be difficult to maintain the steady mass accretion state unless the $Pm$-dependence of MRI-driven turbulence is relatively weak.

Gravitational wave background from sub-luminous GRBs: prospects for second- and third-generation detectors

We assess the detection prospects of a gravitational wave background associated with sub-luminous gamma-ray bursts (SL-GRBs). We assume that the central engines of a significant proportion of these bursts are provided by newly born magnetars and consider two plausible GW emission mechanisms. Firstly, the deformation-induced triaxial GW emission from a newly born magnetar. Secondly, the onset of a secular bar-mode instability, associated with the long lived plateau observed in the X-ray afterglows of many gamma-ray bursts (Corsi & Meszaros 2009a). With regards to detectability, we find that the onset of a secular instability is the most optimistic scenario: under the hypothesis that SL-GRBs associated with secularly unstable magnetars occur at a rate of (48; 80)Gpc^{-3}yr^{-1} or greater, cross-correlation of data from two Einstein Telescopes (ETs) could detect the GW background associated to this signal with a signal-to-noise ratio of 3 or greater after 1 year of observation. Assuming neutron star spindown results purely from triaxial GW emissions, we find that rates of around (130;350)Gpc^{-3}yr^{-1} will be required by ET to detect the resulting GW background. We show that a background signal from secular instabilities could potentially mask a primordial GW background signal in the frequency range where ET is most sen- sitive. Finally, we show how accounting for cosmic metallicity evolution can increase the predicted signal-to-noise ratio for background signals associated with SL-GRBs.

Evidence of different star formation histories for high- and low-luminosity radio galaxies

We present the results of our investigation into the stellar populations of 24 radio galaxies at z≃ 0.5 drawn from four complete, low-frequency-selected radio surveys. We use the strength of the 4000-Å break as an indicator of recent star formation and compare this with radio luminosity, optical spectral classification and morphological classification. We find evidence of different star formation histories for high- and low-luminosity radio sources; our group of low radio luminosity sources (typically Fanaroff–Riley type I sources) has systematically older stellar populations than the higher radio luminosity group. Our sample is also fairly well divided by optical spectral classification. We find that galaxies classified as having low excitation spectra (LEGs) possess older stellar populations than high excitation line objects (HEGs), with the HEGs showing evidence for recent star formation. We also investigate the link between radio morphology, as used by Owen and Laing, and the stellar populations. We find that there is a preference for the ‘fat-double’ sources to have older stellar populations than the ‘classical double’ sources, although this is also linked to these sources lying predominantly in the LEG and HEG categories, respectively. These results are consistent with the hypothesis that HEGs are powered by accretion of cold gas, which could be supplied, for example, by recent mergers, secular instabilities or filamentary cold flows. These processes could also trigger star formation in the host galaxy. The host galaxies of the LEGs do not show evidence for recent star formation and an influx of cold gas and are consistent with being powered by the accretion of the hot phase of the interstellar medium.