scholarly journals Quantification of Sub-Solar Star Ages from the Symmetry of Conjugate Histograms of Spin Period and Angular Velocity

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1519
Author(s):  
Robert E. Criss ◽  
Anne M. Hofmeister
Keyword(s):  
Angular Velocity ◽  
Rotation Period ◽  
Axial Rotation ◽  
Open Clusters ◽  
Interstellar Gas ◽  
Spin Period ◽  
Inverse Models ◽  
Star Production ◽  
Star Ages ◽  
Large Clusters

Empirical laws proposed for the decline in star spin with time have heretofore been tested using ambiguous fitting models. We develop an analytical inverse model that uses histogram data to unequivocally determine the physical law governing how dwarf star spin depends on time (t) and mass (M). We analyze shapes of paired histograms of axial rotation period (П) and angular velocity (ω = 2π/П) to utilize the fact that a variable and its reciprocal are governed by the same physics. Copious data on open clusters are used to test the formula ∂ω/∂t ∝ − ωn where n is unrestricted, and thus covers diverse possibilities. Histogram conjugates for each of 15 clusters with 120 to 812 measurements provide n = 1.13 ± 0.19. Results are independent of initial spin rate, bin size, cluster parameters, and star mass. Notably, 11 large clusters with mostly M-types yield fits with n = 1.07 ± 0.12. Associations behave similarly. Only exponential decay (n = 1) explains the similar shapes of the conjugate histograms for the spin period and angular velocity, despite the asymmetric (inverse) relationship of these variables. This rate law is consistent with viscous dissipation. Forward modeling confirms that n is near unity and further shows that coeval formation of all stars in a cluster does not occur. We therefore explore a constant rate of star production, which is reasonable for tiny stars. Inverse models show that episodic production increases with mass, but is unimportant below ~0.55 MSun. We infer star and cluster ages, and find that star production becomes less regular with time, as interstellar gas and dust are progressively depleted. Our new analytical approach of extracting a physical law from conjugate histograms is general and widely applicable.

scholarly journals Galactic Dynamos and Density Wave Theory

1990 ◽  
Vol 140 ◽  
pp. 135-135
Author(s):  
L Mestel ◽  
K Subramanian
Keyword(s):  
Growth Rate ◽  
Angular Velocity ◽  
Numerical Solutions ◽  
Density Wave ◽  
Wave Theory ◽  
Interstellar Gas ◽  
Global Magnetic Field ◽  
Dynamo Equation ◽  
Density Wave Theory ◽  
Image Position

A steady density wave in the stellar background of a disk–like galaxy is supposed to force a spiral shock wave in the interstellar gas. The jump in vorticity across the shock leads to a locally enhanced helicity, and so to an α–effect which is steady but azimuth–dependent in the frame rotating with the angular velocity ω of the density wave. This is simulated by the adoption of the form for the local dynamo growth rate arising when the standard kinematic dynamo equation is treated by the thin–disk approximation (Ruzmaikin et al 1988). The global magnetic field is proportional to the function Q satisfying where η is the turbulent resistivity (for simplicity assumed uniform) and is the laminar angular velocity of the gas in the inertial frame. We look for solutions of the form where is a global eigen-value, and the non-vanishing of couples all odd or all the even m-values. Anticipating that the strong differential rotation will ensure that in the modes with the largest growth-rate the higher-m parts are weak, the equations are truncated, leaving just a pair in q1, q-1, to describe a basically bisymmetric (m = 1) mode. Approximate treatment by the WKBJ technique suggests that a corotating growing mode (with Γ real and positive) will differ significantly from zero over the range between the points where Numerical solutions have been found for a set of illustrative parameters with corotation occurring at 6.67 kpc, and the turbulence parameters close to those in the M51 mode studied by Ruzmaikin et al which extends over = 1 kpc. Three growing corotating modes were found, the fastest extending for ~ 3 kpc, the other two for over 4 kpc. The first two grow 2-3 times faster, the third somewhat slower, than the M51 mode.

scholarly journals Tidal forces and variability in close binary stars: the β-factor

2003 ◽  
Vol 212 ◽  
pp. 101-105 ◽  
Author(s):  
Gloria Koenigsberger ◽  
Edmundo Moreno ◽  
Fausto Cervantes
Keyword(s):  
Angular Velocity ◽  
Binary Stars ◽  
Rotation Period ◽  
Close Binary ◽  
External Layer ◽  
Stellar Rotation ◽  
Stellar Radius ◽  
Tidal Forces ◽  
Close Binary Stars ◽  
Fixed Set

We present the results of calculations that illustrate the effects, on orbital timescales, produced on the external layer of a star that is in a binary system in which the stellar rotation period is not synchronized with the orbital period. The calculations show how, for a fixed set of parameters, the amplitudes of the oscillations depend on stellar radius and on β, the ratio between the stellar rotation angular velocity and the orbital angular velocity.

scholarly journals The rotation period distribution of the rich Pleiades-age southern open cluster NGC 2516

2020 ◽  
Vol 641 ◽  
pp. A51 ◽  
Author(s):  
D. J. Fritzewski ◽  
S. A. Barnes ◽  
D. J. James ◽  
K. G. Strassmeier
Keyword(s):  
Time Series ◽  
Open Cluster ◽  
Rotation Period ◽  
Open Clusters ◽  
Ccd Photometry ◽  
Activity Diagram ◽  
Cool Star ◽  
Period Distribution ◽  
Rotational Distribution ◽  
Star Rotation

Aims. We wish to measure the cool star rotation period distribution for the Pleiades-age rich open cluster NGC 2516 and use it to determine whether cluster-to-cluster variations exist in otherwise identical open clusters. Methods. We obtained 42 d-long time-series CCD photometry of NGC 2516 in the V and Ic filters using the Yale 1 m telescope at CTIO and performed a number of related analyses, including PSF-based time-series photometry. Our data are complemented with additional information from several photometric datasets, literature radial velocities, and Gaia DR2 astrometry. All available data are used to construct an integrated membership list for NGC 2516, containing 844 stars in our ≈1° field of view. Results. We derived 308 rotation periods for late-F to mid-M cluster members from our photometry. We identified an additional 247 periodic M dwarf stars from a prior study as cluster members, and used these to construct a 555-star rotation period distribution for NGC 2516. The colour-period diagram (in multiple colours) has almost no outliers and exhibits the anticipated triangular shape, with a diagonal slow rotator sequence that is preferentially occupied by the warmer stars along with a flat fast rotator sequence that is preferentially populated by the cooler cluster members. We also find a group of extremely slowly rotating M dwarfs (10 d ≲ Prot ≲ 23 d), forming a branch in the colour-period diagram which we call the “extended slow rotator sequence”. This, and other features of the rotational distribution can also be found in the Pleiades, making the colour-period diagrams of the two clusters nearly indistinguishable. A comparison with the well-studied (and similarly aged) open cluster M 35 indicates that the cluster’s rotational distribution is also similarly indistinguishable from that of NGC 2516. Those for the open clusters M 50 and Blanco 1 are similar, but data issues for those clusters make the comparisons somewhat more ambiguous. Nevertheless, we demonstrate the existence of a representative zero-age main sequence rotational distribution and provide a simple colour-independent way to represent it. We perform a detailed comparison of the NGC 2516 rotation period data with a number of recent rotational evolution models. Using X-ray data from the literature, we also construct the first rotation-activity diagram for solar-type stars in NGC 2516, one that we find is essentially indistinguishable from those for the Pleiades and Blanco 1. Conclusions. The two clusters NGC 2516 and Pleiades can be considered twins in terms of stellar rotation and related properties (and M 35, M 50, and Blanco 1 are similar), suggesting that otherwise identical open clusters also have intrinsically similar cool star rotation and activity distributions.

scholarly journals Evolution of star–planet systems under magnetic braking and tidal interaction

2019 ◽  
Vol 621 ◽  
pp. A124 ◽  
Author(s):  
M. Benbakoura ◽  
V. Réville ◽  
A. S. Brun ◽  
C. Le Poncin-Lafitte ◽  
S. Mathis
Keyword(s):  
Ab Initio ◽  
Stellar Wind ◽  
Structural Changes ◽  
Rotation Period ◽  
Major Axis ◽  
Orbital Evolution ◽  
Open Clusters ◽  
Stellar Rotation ◽  
Semi Major Axis ◽  
Tidal Interaction

Context.With the discovery over the last two decades of a large diversity of exoplanetary systems, it is now of prime importance to characterize star–planet interactions and how such systems evolve.Aims.We address this question by studying systems formed by a solar-like star and a close-in planet. We focus on the stellar wind spinning down the star along its main-sequence phase and tidal interaction causing orbital evolution of the systems. Despite recent significant advances in these fields, all current models use parametric descriptions to study at least one of these effects. Our objective is to introduce ab initio prescriptions of the tidal and braking torques simultaneously, so as to improve our understanding of the underlying physics.Methods.We develop a one-dimensional (1D) numerical model of coplanar circular star–planet systems taking into account stellar structural changes, wind braking, and tidal interaction and implement it in a code called ESPEM. We follow the secular evolution of the stellar rotation and of the semi-major axis of the orbit, assuming a bilayer internal structure for the former. After comparing our predictions to recent observations and models, we perform tests to emphasize the contribution of ab initio prescriptions. Finally, we isolate four significant characteristics of star–planet systems: stellar mass, initial stellar rotation period, planetary mass and initial semi-major axis; and browse the parameter space to investigate the influence of each of them on the fate of the system.Results.Our secular model of stellar wind braking accurately reproduces the recent observations of stellar rotation in open clusters. Our results show that a planet can affect the rotation of its host star and that the resulting spin-up or spin-down depends on the orbital semi-major axis and on the joint influence of magnetic and tidal effects. The ab initio prescription for tidal dissipation that we used predicts fast outward migration of massive planets orbiting fast-rotating young stars. Finally, we provide the reader with a criterion based on the characteristics of the system that allows us to assess whether or not the planet will undergo orbital decay due to tidal interaction.

scholarly journals Strong evidences for a nonextensive behavior of the rotation period in open clusters

2014 ◽  
Vol 108 (3) ◽  
pp. 39001 ◽  
Author(s):  
D. B. de Freitas ◽  
M. M. F. Nepomuceno ◽  
B. B. Soares ◽  
J. R. P. Silva
Keyword(s):  
Rotation Period ◽  
Open Clusters

scholarly journals Ekman pumping in compact astrophysical bodies

1996 ◽  
Vol 312 ◽  
pp. 327-340 ◽  
Author(s):  
Mark Abney ◽  
Richard I. Epstein
Keyword(s):  
Angular Velocity ◽  
Viscous Fluid ◽  
Thin Layer ◽  
Neutron Stars ◽  
Abrupt Change ◽  
Density Stratification ◽  
Ekman Pumping ◽  
Bounding Surface ◽  
Spin Period ◽  
Astrophysical Objects

We examine the dynamics of a rotating viscous fluid following an abrupt change in the angular velocity of the solid bounding surface. We include the effects of a density stratification and compressibility which are important in astrophysical objects such as neutron stars. We confirm and extend the conclusions of previous studies that stratification restricts the Ekman pumping process to a relatively thin layer near the boundary, leaving much of the interior fluid unaffected. We find that finite compressibility further inhibits Ekman pumping by decreasing the extent of the pumped layer and by increasing the time for spin-up. The results of this paper are important for interpreting the spin period discontinuities (‘glitches’) observed in rotating neutron stars.

On the dynamical theory of the rotation of the earth. II. The effect of precession on the motion of the liquid core

1953 ◽  
Vol 49 (3) ◽  
pp. 498-515 ◽  
Author(s):  
H. Bondi ◽  
R. A. Lyttleton
Keyword(s):  
Angular Velocity ◽  
Liquid Core ◽  
Rotation Period ◽  
Steady Motion ◽  
Dynamical Theory ◽  
Rate Of Change ◽  
Body Motion ◽  
Angular Velocity Vector ◽  
The Core ◽  
The Earth

In an earlier paper of the same general title (1) the possibility that the core of the Earth, in view of its supposed liquid nature, does not partake of the rigid-body motion of the outer shell was discussed with particular reference to the secular diminution of the angular velocity. In addition to this small rate of change of the magnitude of the angular velocity vector of the shell there occur changes in its direction consisting of the precession and nutation, but all the rates of change therein involved are small. The secular retardation takes place with extreme slowness, the nutations involve deviations of the axis with small angular amplitudes, while the precession, though of large angular amplitude, is of very long period compared with the rotation period of the Earth. Accordingly, it may be supposed that the effects of these various changes in the angular velocity can be considered separately in their relation to the motion within the core, and it is the object of this paper to give an account of our investigation into what may be termed for brevity the precession problem. It should perhaps be stated at the outset that the work does not constitute a solution of the problem, which our studies have led us to believe is one of the utmost mathematical difficulty presenting features of an exceptional character in hydro-dynamic theory. After first obtaining the equations of steady motion applicable to the interior, and those applicable to the boundary layer, the solution of the latter equations has been obtained; but in respect of the former equations we have been able to carry the question of the interior motion only as far as showing that no motion representable everywhere by analytic functions and consistent with the boundary conditions is possible. The investigation strongly suggests that no steady-state motion of a permanent character is possible for the interior, though the precise nature of the motion that actually occurs poses a problem of special interest from a hydrodynamic standpoint, but it is one to which we are not able to arrive at any definite answer at present. Without making any progress with the problem thus produced, the paper nevertheless makes clear the inherent difficulties of the problem and also serves to emphasize the inadequacy of any simplified mode of attack assuming classical fluid and resembling, for example, Poincaré's method for the nutation problem adopted by Lamb (3). Thus despite its incompleteness it seemed worth while to publish some account of such progress with these highly interesting questions as we have been able to make.

scholarly journals Rotation in Close Binaries (Review Paper)

1970 ◽  
Vol 4 ◽  
pp. 132-146
Author(s):  
Miroslav Plavec
Keyword(s):  
Angular Velocity ◽  
Binary Systems ◽  
Review Paper ◽  
Axial Rotation ◽  
Linear Velocity ◽  
Fundamental Question ◽  
The Other ◽  
Close Binaries ◽  
Average Period ◽  
Orbital Revolution

When studying the axial rotation of the components of binary systems, we ask the following fundamental question: How much is axial rotation affected by the other star? In particular, is there any synchronism between the periods of axial rotation and orbital revolution?Thus in fact we are more interested here in the angular than in the linear velocity of rotation. It was pointed out by McNally (1965) that the angular velocity of rotation reaches its maximum near A5 and drops off rather rapidly on both sides so that the GOV and 05V stars have approximately the same average period of rotation. The accompanying Table I is an adaptation of McNally’s figures.

Motion of spheroid particles in shear flow with inertia

2014 ◽  
Vol 749 ◽  
pp. 145-166 ◽  
Author(s):  
Wenbin Mao ◽  
Alexander Alexeev
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Shear Flow ◽  
Rotation Period ◽  
Reynolds Numbers ◽  
Stokes Number ◽  
Simple Shear Flow ◽  
Fluid Inertia ◽  
Particle Rotation ◽  
Particle Inertia

AbstractIn this article, we investigate the motion of a solid spheroid particle in a simple shear flow. Using a lattice Boltzmann method, we examine individual effects of fluid inertia and particle rotary inertia as well as their combination on the dynamics and trajectory of spheroid particles at low and moderate Reynolds numbers. The motion of a single spheroid is shown to be dependent on the particle Reynolds number, particle aspect ratio, particle initial orientation and the Stokes number. Spheroids with random initial orientations are found to drift to stable orbits influenced by fluid inertia and/or particle inertia. Specifically, prolate spheroids drift towards the tumbling mode of motion, whereas oblate spheroids drift to the rolling mode. The rotation period and the variation of angular velocity of tumbling spheroids decrease as Stokes number increases. With increasing Reynolds number, both the maximum and minimum values of angular velocity decrease, whereas the particle rotation period increases. We show that particle inertia does not affect the hydrodynamic torque on the particle. We also demonstrate that superposition can be used to estimate the combined effect of fluid inertia and particle inertia on the dynamics of spheroid particles at sufficiently low Reynolds numbers.

Sign in / Sign up

Export Citation Format

Share Document