Redistribution Of Angular Momentum Research Articles

Testing tidal theory for evolved stars by using red giant binaries observed by Kepler

Abstract Tidal interaction governs the redistribution of angular momentum in close binary stars and planetary systems and determines the systems evolution towards the possible equilibrium state. Turbulent friction acting on the equilibrium tide in the convective envelope of low-mass stars is known to have a strong impact on this exchange of angular momentum in binaries. Moreover, theoretical modelling in recent literature as well as presented in this paper suggests that the dissipation of the dynamical tide, constituted of tidal inertial waves propagating in the convective envelope, is weak compared to the dissipation of the equilibrium tide during the red giant phase. This prediction is confirmed when we apply the equilibrium-tide formalism developed by Zahn, Verbunt & Phinney, and Remus, Mathis & Zahn on to the sample of all known red giant binaries observed by the NASA Kepler mission. Moreover, the observations are adequately explained by only invoking the equilibrium tide dissipation. Such ensemble analysis also benefits from the seismic characterization of the oscillating components and surface rotation rates. Through asteroseismology, previous claims of the eccentricity as an evolutionary state diagnostic are discarded. This result is important for our understanding of the evolution of multiple star and planetary systems during advanced stages of stellar evolution.

Dynamics of merging: post-merger mixing and relaxation of an Illustris galaxy

During the merger of two galaxies, the resulting system undergoes violent relaxation and seeks stable equilibrium. However, the details of this evolution are not fully understood. Using Illustris simulation, we probe two physically related processes, mixing and relaxation. Though the two are driven by the same dynamics—global time-varying potential for the energy, and torques caused by asymmetries for angular momentum—we measure them differently. We define mixing as the redistribution of energy and angular momentum between particles of the two merging galaxies. We assess the degree of mixing as the difference between the shapes of their energy distributions, N(E)s, and their angular momentum distributions, N(L2)s. We find that the difference is decreasing with time, indicating mixing. To measure relaxation, we compare N(E) of the newly merged system to N(E) of a theoretical prediction for relaxed collisionless systems, DARKexp, and witness the system becoming more relaxed, in the sense that N(E) approaches DARKexp N(E). Because the dynamics driving mixing and relaxation are the same, the timescale is similar for both. We measure two sequential timescales: a rapid, 1 Gyr phase after the initial merger, during which the difference in N(E) of the two merging halos decreases by ∼ 80%, followed by a slow phase, when the difference decreases by ∼ 50% over ∼ 8.5 Gyrs. This is a direct measurement of the relaxation timescale. Our work also draws attention to the fact that when a galaxy has reached Jeans equilibrium it may not yet have reached a fully relaxed state given by DARKexp, in that it retains information about its past history. This manifests itself most strongly in stars being centrally concentrated. We argue that it is particularly difficult for stars, and other tightly bound particles, to mix because they have less time to be influenced by the fluctuating potential, even across multiple merger events.

Hydrodynamical Aspects of the Formation of Spiral–Vortical Structures in Rotating Gaseous Disks

This paper is dedicated to numerical simulations of spiral–vortical structures in rotating gaseous disks using a simple model based on two-dimensional, non-stationary, barotropic Euler equations with a body force. The results suggest the possibility of a purely hydrodynamical basis for the formation and evolution of such structures. New, axially symmetric, stationary solutions of these equations are derived that modify known approximate solutions. These solutions with added small perturbations are used as initial data in the non-stationary problem, whose solution demonstrates the formation of density arms with bifurcation. The associated redistribution of angular momentum is analyzed. The correctness of laboratory experiments using shallow water to describe the formation of large-scale vortical structures in thin gaseous disks is confirmed. The computations are based on a special quasi-gas-dynamical regularization of the Euler equations in polar coordinates.

On the Papaloizou–Pringle instability in tidal disruption events

We demonstrate that the compact, thick disc formed in a tidal disruption event may be unstable to non-axisymmetric perturbations in the form of the Papaloizou-Pringle instability. We show this can lead to rapid redistribution of angular momentum that can be parameterised in terms of an effective Shakura-Sunyaev $\alpha$ parameter. For remnants that have initially weak magnetic fields, this may be responsible for driving mass accretion prior to the onset of the magneto-rotational instability. For tidal disruptions around a $10^6$ M$_{\odot}$ black hole, the measured accretion rate is super-Eddington but is not sustainable over many orbits. We thus identify a method by which the torus formed in tidal disruption event may be significantly accreted before the magneto-rotational instability is established.

Forming disc galaxies in major mergers – III. The effect of angular momentum on the radial density profiles of disc galaxies

We study the effect of angular momentum on the surface density profiles of disc galaxies, using high resolution simulations of major mergers whose remnants have downbending radial density profiles (type II). As described in the previous papers of this series, in this scenario, most of the disc mass is acquired after the collision via accretion from a hot gaseous halo. We find that the inner and outer disc scalelengths, as well as the break radius, correlate with the total angular momentum of the initial merging system, and are larger for high angular momentum systems. We follow the angular momentum redistribution in our simulated galaxies, and find that, like the mass, the disc angular momentum is acquired via accretion, i.e. to the detriment of the gaseous halo. Furthermore, high angular momentum systems give more angular momentum to their discs, which affects directly their radial density profile. Adding simulations of isolated galaxies to our sample, we find that the correlations are valid also for disc galaxies evolved in isolation. We show that the outer part of the disc at the end of the simulation is populated mainly by inside-out stellar migration, and that in galaxies with higher angular momentum, stars travel radially further out. This, however, does not mean that outer disc stars (in type II discs) were mostly born in the inner disc. Indeed, generally the break radius increases over time, and not taking this into account leads to overestimating the number of stars born in the inner disc.

Implications of the generation of internal gravity waves by penetrative convection for the internal rotation evolution of low-mass stars

Due to the space-borne missions CoRoT and Kepler , noteworthy breakthroughs have been made in our understanding of stellar evolution, and in particular about the angular momentum redistribution in stellar interiors. Indeed, the high-precision seismic data provide with the measurement of the mean core rotation rate for thousands of low-mass stars from the subgiant branch to the red giant branch. All these observations exhibit much lower core rotation rates than expected by current stellar evolution codes and they emphasize the need for an additional transport process. In this framework, internal gravity waves (herefater, IGW) could play a signifivative role since they are known to be able to transport angular momentum. In this work, we estimate the effciency of the transport by the IGW that are generated by penetrative convection at the interface between the convective and the radiative regions. As a first step, this study is based on the comparison between the timescale for the waves to modify a given rotation profile and the contraction/expansion timescale throughout the radiative zone of 1.3M⊙ stellar models. We show that IGW, on their own, are ineffcient to slow down the core rotation of stars on the red giant branch, where the radiative damping becomes strong enough and prevent the IGW from reaching the innermost layers. However, we find that IGW generated by penetrative convection could effciently modify the core rotation of subgiant stars as soon as the amplitude of the radial differential rotation between the core and the base of the convective zone is high enough, with typical values close to the observed rotation rates in these stars. This result argues for the necessity to account for IGW generated by penetrative convection in stellar modeling and in the angular momentum redistribution issue.

Libration of Strongly‐Oriented Polar Molecules inside a Superfluid

We study a polar molecule immersed in a superfluid environment, such as a helium nanodroplet or a Bose-Einstein condensate, in the presence of a strong electrostatic field. We show that coupling of the molecular pendular motion, induced by the field, to the fluctuating bath leads to formation of pendulons-spherical harmonic librators dressed by a field of many-particle excitations. We study the behavior of the pendulon in a broad range of molecule-bath and molecule-field interaction strengths, and reveal that its spectrum features a series of instabilities which are absent in the field-free case of the angulon quasiparticle. Furthermore, we show that an external field allows to fine-tune the positions of these instabilities in the molecular rotational spectrum. This opens the door to detailed experimental studies of redistribution of orbital angular momentum in many-particle systems.

Light or heavy supermassive black hole seeds: the role of internal rotation in the fate of supermassive stars

Supermassive black holes are a key ingredient of galaxy evolution. However, their origin is still highly debated. In one of the leading formation scenarios, a black hole of ∼100 M⊙ results from the collapse of the inner core of a supermassive star (≳104–5 M⊙), created by the rapid accumulation (≳0.1 M⊙ yr−1) of pristine gas at the centre of newly formed galaxies at z ∼ 15. The subsequent evolution is still speculative: the remaining gas in the supermassive star can either directly plunge into the nascent black hole or part of it can form a central accretion disc, whose luminosity sustains a surrounding, massive, and nearly hydrostatic envelope (a system called a ‘quasi-star’). To address this point, we consider the effect of rotation on a quasi-star, as angular momentum is inevitably transported towards the galactic nucleus by the accumulating gas. Using a model for the internal redistribution of angular momentum that qualitatively matches results from simulations of rotating convective stellar envelopes, we show that quasi-stars with an envelope mass greater than a few 105 M| $_{\odot } \times (\rm black\ hole\ mass/100\,\mathrm{M}_{\odot })^{0.82}$ | have highly sub-Keplerian gas motion in their core, preventing gas circularization outside the black hole's horizon. Less massive quasi-stars could form but last for only ≲104 yr before the accretion luminosity unbinds the envelope, suppressing the black hole growth. We speculate that this might eventually lead to a dual black hole seed population: (i) massive (>104 M⊙) seeds formed in the most massive (>108 M⊙) and rare haloes; (ii) lighter (∼102 M⊙) seeds to be found in less massive and therefore more common haloes.

Global multifluid simulations of the magnetorotational instability in radially stratified protoplanetary discs

The redistribution of angular momentum is a long standing problem in our understanding of protoplanetary disk (PPD) evolution. The magnetorotational instability (MRI) is considered a likely mechanism. We present the results of a study involving multifluid global simulations including Ohmic dissipation, ambipolar diffusion and the Hall effect in a dynamic, self-consistent way. We focus on the turbulence resulting from the non-linear development of the MRI in radially stratified PPDs and compare with ideal MHD simulations. In the multifluid simulations the disk is initially set up to transition from a weak Hall dominated regime, where the Hall effect is the dominant non-ideal effect but approximately the same as or weaker than the inductive term, to a strong Hall dominated regime, where the Hall effect dominates the inductive term. As the simulations progress a substantial portion of the disk develops into a weak Hall dominated disk. We find a transition from turbulent to laminar flow in the inner regions of the disk, but without any corresponding overall density feature. We introduce a dimensionless parameter, $\alpha_\mathrm{RM}$, to characterise accretion with $\alpha_\mathrm{RM} \gtrsim 0.1$ corresponding to turbulent transport. We calculate the eddy turnover time, $t_\mathrm{eddy}$, and compared this with an effective recombination timescale, $t_\mathrm{rcb}$, to determine whether the presence of turbulence necessitates non-equilibrium ionisation calculations. We find that $t_\mathrm{rcb}$ is typically around three orders of magnitude smaller than $t_\mathrm{eddy}$. Also, the ionisation fraction does not vary appreciably. These two results suggest that these multifluid simulations should be comparable to single fluid non-ideal simulations.

THE ANGULAR MOMENTUM DISTRIBUTION AND BARYON CONTENT OF STAR-FORMING GALAXIES AT z ∼ 1–3*

ABSTRACT We analyze the angular momenta of massive star-forming galaxies (SFGs) at the peak of the cosmic star formation epoch (z ∼ 0.8–2.6). Our sample of ∼360 log(M */M ⊙) ∼ 9.3–11.8 SFGs is mainly based on the KMOS3D and SINS/zC-SINF surveys of Hα kinematics, and collectively provides a representative subset of the massive star-forming population. The inferred halo scale angular momentum distribution is broadly consistent with that theoretically predicted for their dark matter halos, in terms of mean spin parameter ∼ 0.037 and its dispersion (σ logλ ∼ 0.2). Spin parameters correlate with the disk radial scale and with their stellar surface density, but do not depend significantly on halo mass, stellar mass, or redshift. Our data thus support the long-standing assumption that on average, even at high redshifts, the specific angular momentum of disk galaxies reflects that of their dark matter halos (j d = j DM). The lack of correlation between λ × (j d /j DM) and the nuclear stellar density Σ*(1 kpc) favors a scenario where disk-internal angular momentum redistribution leads to “compaction” inside massive high-redshift disks. For our sample, the inferred average stellar to dark matter mass ratio is ∼2%, consistent with abundance matching results. Including the molecular gas, the total baryonic disk to dark matter mass ratio is ∼5% for halos near 1012 M ⊙, which corresponds to 31% of the cosmologically available baryons, implying that high-redshift disks are strongly baryon dominated.

Common envelope events with low-mass giants: understanding the transition to the slow spiral-in

We present a three-dimensional (3D) study of common envelope events (CEEs) to provide a foundation for future one-dimensional (1D) methods to model the self-regulated phase of a CEE. The considered CEEs with a low-mass red giant end with one of three different outcomes -- merger, slow spiral-in, or prompt formation of a binary. To understand which physical processes determine different outcomes, and to evaluate how well 1D simulations model the self-regulated phase of a CEE, we introduce tools that map our 3D models to 1D profiles. We discuss the differences in the angular momentum and energy redistribution in 1D and 3D codes. We identified four types of ejection processes: the pre-plunge-in ejection, the outflow during the plunge-in, the outflow driven by recombination, and the ejection triggered by a contraction of the circumbinary envelope. Significant mass is lost in all cases, including the mergers. Therefore a self-regulated spiral-in can start only with a strongly reduced envelope mass. We derive the condition to start a recombination outflow, which can proceed either as a runaway or a stationary outflow. We show that the way the energy of the inspiraling companion is added to the envelope in 1D studies intensifies the envelope's entropy increase, alters the start of the recombination outflow, and leads to different outcomes in 1D and 3D studies. The steady recombination outflow may dispel most of the envelope in all slow spiral-in cases, making the existence of a long-term self-regulated phase debatable, at least for low-mass giant donors.

Tides and angular momentum redistribution inside low-mass stars hosting planets: a first dynamical model

We introduce a general mathematical framework to model the internal transport of angular momentum in a star hosting a close-in planetary/stellar companion. By assuming that the tidal and rotational distortions are small and that the deposit/extraction of angular momentum induced by stellar winds and tidal torques are redistributed solely by an effective eddy-viscosity that depends on the radial coordinate, we can formulate the model in a completely analytic way. It allows us to compute simultaneously the evolution of the orbit of the companion and of the spin and the radial differential rotation of the star. An illustrative application to the case of an F-type main-sequence star hosting a hot Jupiter is presented. The general relevance of our model to test more sophisticated numerical dynamical models and to study the internal rotation profile of exoplanet hosts, submitted to the combined effects of tides and stellar winds, by means of asteroseismology are discussed.

THE IMPACT OF STELLAR FEEDBACK ON THE STRUCTURE, SIZE, AND MORPHOLOGY OF GALAXIES IN MILKY-WAY-SIZED DARK MATTER HALOS

ABSTRACT We use cosmological zoom-in simulations of galaxy formation in a Milky-Way-sized halo started from identical initial conditions to investigate the evolution of galaxy sizes, baryon fractions, morphologies, and angular momenta in runs with different parameters of the star formation–feedback cycle. Our fiducial model with a high local star formation efficiency, which results in efficient feedback, produces a realistic late-type galaxy that matches the evolution of basic properties of late-type galaxies: stellar mass, disk size, morphology dominated by a kinematically cold disk, stellar and gas surface density profiles, and specific angular momentum. We argue that feedback’s role in this success is twofold: (1) removal of low angular momentum gas, and (2) maintaining a low disk-to-halo mass fraction, which suppresses disk instabilities that lead to angular momentum redistribution and a central concentration of baryons. However, our model with a low local star formation efficiency, but large energy input per supernova, chosen to produce a galaxy with a similar star formation history as our fiducial model, leads to a highly irregular galaxy with no kinematically cold component, overly extended stellar distribution, and low angular momentum. This indicates that only when feedback is allowed to become vigorous via locally efficient star formation in dense cold gas do resulting galaxy sizes, gas/stellar surface density profiles, and stellar disk angular momenta agree with observed z = 0 galaxies.

Angular momentum transport efficiency in post-main sequence low-mass stars

Context. Using asteroseismic techniques, it has recently become possible to probe the internal rotation profile of low-mass (~1.1-1.5 Msun) subgiant and red giant stars. Under the assumption of local angular momentum conservation, the core contraction and envelope expansion occurring at the end of the main sequence would result in a much larger internal differential rotation than observed. This suggests that angular momentum redistribution must be taking place in the interior of these stars. Aims. We investigate the physical nature of the angular momentum redistribution mechanisms operating in stellar interiors by constraining the efficiency of post-main sequence rotational coupling. Methods. We model the rotational evolution of a 1.25 Msun star using the Yale Rotational stellar Evolution Code. Our models take into account the magnetic wind braking occurring at the surface of the star and the angular momentum transport in the interior, with an efficiency dependent on the degree of internal differential rotation. Results. We find that models including a dependence of the angular momentum transport efficiency on the radial rotational shear reproduce very well the observations. The best fit of the data is obtained with an angular momentum transport coefficient scaling with the ratio of the rotation rate of the radiative interior over that of the convective envelope of the star as a power law of exponent ~3. This scaling is consistent with the predictions of recent numerical simulations of the Azimuthal Magneto-Rotational Instability. Conclusions. We show that an angular momentum transport process whose efficiency varies during the stellar evolution through a dependence on the level of internal differential rotation is required to explain the observed post-main sequence rotational evolution of low-mass stars.

Generation of internal gravity waves by penetrative convection

The rich harvest of seismic observations over the past decade provides evidence of angular momentum redistribution in stellar interiors that is not reproduced by current evolution codes. In this context, transport by internal gravity waves can play a role and could explain discrepancies between theory and observations. The efficiency of the transport of angular momentum by waves depends on their driving mechanism. While excitation by turbulence throughout the convective zone has already been investigated, we know that penetrative convection into the stably stratified radiative zone can also generate internal gravity waves. Therefore, we aim at developing a semianalytical model to estimate the generation of IGW by penetrative plumes below an upper convective envelope. We derive the wave amplitude considering the pressure exerted by an ensemble of plumes on the interface between the radiative and convective zones as source term in the equation of momentum. We consider the effect of a thermal transition from a convective gradient to a radiative one on the transmission of the wave into the radiative zone. The plume-induced wave energy flux at the top of the radiative zone is computed for a solar model and is compared to the turbulence-induced one. We show that, for the solar case, penetrative convection generates waves more efficiently than turbulence and that plume-induced waves can modify the internal rotation rate on shorter time scales. We also show that a smooth thermal transition significatively enhances the wave transmission compared to the case of a steep transition. We conclude that driving by penetrative convection must be taken into account as much as turbulence-induced waves for the transport of internal angular momentum.

Varying polarization and spin angular momentum flux of radially polarized beams by anisotropic Kerr media.

Light fields with structured polarization distribution interacting with structured media will result in many novel optical effects in both the linear and nonlinear regimes. In this work, we report a theoretical investigation of both vectorial self-diffraction behaviors and polarization evolution characteristics of a radially polarized beam induced by anisotropic Kerr nonlinearity. By taking the polarization-orientation dependence of the third-order refractive nonlinearity, we study the far-field vectorial self-diffraction patterns of the radially polarized beam using the vectorial Rayleigh-Sommerfeld formulas. Numerical results reveal that the self-diffraction patterns with a four-fold rotational symmetry exhibit hybrid states of polarization. Moreover, the interaction of radially polarized beams with the anisotropic nonlinear Kerr media leads to the redistribution of the spin angular momentum (SAM) flux in the far-field plane. The presented work opens up new avenues for varying polarization and SAM through anisotropic optical nonlinearity.

Vector optical fields broken in the spatial frequency domain

We theoretically and experimentally explore the redistribution of polarization states and orbital angular momentum (OAM) in the output plane, induced by the symmetry breaking in the spatial frequency domain. When the vector fields are obstructed by sector-shaped filters in the spatial frequency domain, the local polarization states in the output plane undergo an abrupt transition from linear to circular polarization. The results reveal the polarization-dependent splitting and the appearance of a series of opposite OAMs in the output plane. We also find the self-healing effect of the vector fields broken in the spatial frequency domain and further explore its potential application. If the vector optical fields are used for information transferring or for imaging, even if the optical field carrying the information or image is partially blocked, the complete information or image can still be obtained, implying that which may increase the robustness of the information transferring and the imaging.

Nonaxisymmetric instabilities in self-gravitating disks III. Angular momentum transport

We follow the development of nonaxisymmetric instabilities of self-gravitating disks from the linear regime to the nonlinear regime. Particular attention is paid to comparison of nonlinear simulation results with previous linear and quasi-linear modeling results to study the mass and angular momentum transport driven by nonaxisymmetric disk instabilities. Systems with star-to-disk mass ratios of $M_{*}/M_{d} = 0.1$ and 5 and inner-to-outer disk radius ratios of $r_{-}/r_{+} = 0.47$ to 0.66 are investigated. In disks where self-gravity is important, systems with small $M_{*}/M_{d}$ and large $r_{-}/r_{+}$ , Jeans-like J modes are dominant and the gravitational stress drives angular momentum transport. In disks where self-gravity is weak, systems with large $M_{*}/M_{d}$ and large $r_{-}/r_{+}$ , shear-driven P modes dominate and the Reynolds stress drives angular momentum transport. In disks where self-gravity is intermediate in strength between disks where P modes dominate and disks where J modes dominate, I modes control the evolution of the system and the Reynolds and gravitational stresses both play important roles in the angular momentum transport. In all cases, redistribution of angular momentum takes place on the characteristic disk timescale defined as the orbital period at the location of maximum density in the disk midplane. The disk susceptible to one-armed modes behaves differently than disks dominated by multi-armed spirals. Coupling between the star and the disk driven by one-armed modes leads to angular momentum transfer between the star and disk even when instability is in the linear regime. All modes drive spreading of the disk material and eventually accretion onto the star. The disks dominated by an I mode and one-armed mode do not lead to prompt fission or fragmentation. The J mode dominated disk fragments after instability develops.

Seismic evidence for a weak radial differential rotation in intermediate-mass core helium burning stars

The detection of mixed modes that are split by rotation in Kepler red giants has made it possible to probe the internal rotation profiles of these stars, which brings new constraints on the transport of angular momentum in stars. Mosser et al. (2012) have measured the rotation rates in the central regions of intermediate-mass core helium burning stars (secondary clump stars). Our aim was to exploit& the rotational splittings of mixed modes to estimate the amount of radial differential rotation in the interior of secondary clump stars using Kepler data, in order to place constraints on angular momentum transport in intermediate-mass stars. We selected a subsample of Kepler secondary clump stars with mixed modes that are clearly rotationally split. By applying a thorough statistical analysis, we showed that the splittings of both gravity-dominated modes (trapped in central regions) and p-dominated modes (trapped in the envelope) can be measured. We then used these splittings to estimate the amount of differential rotation by using inversion techniques and by applying a simplified approach based on asymptotic theory (Goupil et al. 2013). We obtained evidence for a weak radial differential rotation for six of the seven targets that were selected, with the central regions rotating $1.8\pm0.3$ to $3.2\pm1.0$ times faster than the envelope. The last target was found to be consistent with a solid-body rotation. This demonstrates that an efficient redistribution of angular momentum occurs after the end of the main sequence in the interior of intermediate-mass stars, either during the short-lived subgiant phase, or once He-burning has started in the core. In either case, this should bring constraints on the angular momentum transport mechanisms that are at work.

Angular momentum redistribution by mixed modes in evolved low-mass stars

Seismic observations by the space-borne mission \emph{Kepler} have shown that the core of red giant stars slows down while evolving, requiring an efficient physical mechanism to extract angular momentum from the inner layers. Current stellar evolution codes fail to reproduce the observed rotation rates by several orders of magnitude, and predict a drastic spin-up of red giant cores instead. New efficient mechanisms of angular momentum transport are thus required. In this framework, our aim is to investigate the possibility that mixed modes extract angular momentum from the inner radiative regions of evolved low-mass stars. To this end, we consider the Transformed Eulerian Mean (TEM) formalism, introduced by Andrews \& McIntyre (1978), that allows us to consider the combined effect of both the wave momentum flux in the mean angular momentum equation and the wave heat flux in the mean entropy equation as well as their interplay with the meridional circulation. In radiative layers of evolved low-mass stars, the quasi-adiabatic approximation, the limit of slow rotation, and the asymptotic regime can be applied for mixed modes and enable us to establish a prescription for the wave fluxes in the mean equations. The formalism is finally applied to a $1.3 M_\odot$ benchmark model, representative of observed CoRoT and \emph{Kepler} oscillating evolved stars. We show that the influence of the wave heat flux on the mean angular momentum is not negligible and that the overall effect of mixed modes is to extract angular momentum from the innermost region of the star. A quantitative and accurate estimate requires realistic values of mode amplitudes. This is provided in a companion paper.