Rotation Law Research Articles

Milky Way Rotation Models from Neutral Hydrogen and Molecular Clouds: Galactic Constants, Common Details and Differences

Kinematic data from neutral hydrogen observations provide information to solve the interdependent problems of the determination of the main Galactic constants (the Solar-Galactic center distance R0, the Oort constant A and others) and the Galactic rotation curve (Nikiforov & Petrovskaya 1994, hereafter NP94, and references therein). However, in the standard method for finding R0 by comparing the rotations of HI clouds and some other objects (typically HII regions/CO clouds), the kinematic model, constructed typically solely from HI data, is considered to be the same for both galactic subsystems (e.g. Merrifield 1992). In practice a discrepancy between their rotation curves can produce strongly erroneous results (Merrifield 1992, NP94). Establishing the common rotation law from HI plus HII/CO data in NP94 is only a part of attacking the problem.

Self‐similar Viscous Accretion and Growth of the Central Core in Self‐gravitating Disks

Unsteady viscous accretion in self-gravitating disks is investigated. Taking into account the growth of the central point mass, a series of self-similar solutions is derived for rotating isothermal disks. These solutions represent the inside-out evolution after central core formation. Solutions are specified by the nondimensional parameters α and Q, where α is the Shakura and Sunyaev viscous parameter and Q is the Toomre stability parameter. As a core mass increases, the rotation law changes from flat rotation to Keplerian rotation in the inner disk. In addition to the central point mass, the inner disk grows by mass accumulation due to the differing mass accretion rates in the inner and outer radii. The mass accretion rate onto the central core is found to be 3αc/QG for a variety of outer flows. We show that possibly stable solutions with Q ≳ 1 exist for a wide range of α.

Collision broadening of rotational transitions in the O2A band by molecular perturbers

Fourier transform spectroscopy was utilized to record absorption line shapes for rotational transitions in the magnetic dipole allowed b1Σg+←X3Σg− system of O2. Broadening coefficients were determined for 42 rotational transitions in the (0,0) vibrational band spanning the spectral range from 13020cm−1 to 13170cm−1. Voigt profiles were fit to the experimental line shapes using a nonlinear least-squares technique, and the Lorentzian half-width at half-maximum values were determined as a function of bath gas pressure. The pressure broadening coefficients for O2 by O2, CO, N2, CO2, and SF6 were obtained with uncertainties of less than 5% and the values showed a significant dependence on rotational quantum number. These rotational level dependencies were modeled using both angular momentum and energy-based rotational energy transfer fitting laws. We found both the ECS-P and the EPGL-0 fitting laws adequately represented the line broadening cross sections.

Magnetization and nature of the rotation of the solar convective zone

An analysis is made of adiabatic magnetized differentially rotating structures of the stellar convective zone obtained by minimizing the production of entropy. The change in the law of rotation when one type of magnetic field is replaced by another (for example, a toroidal field by a poloidal one) is studied. It is found that for the latitude distribution of the rotation observed on the Sun, the variation in the latitude gradient of the angular rotation speed is comparatively small for this change in fields. This condition facilitates the establishment of cyclic variations in the field. In a configuration in which the equatorial layers rotate faster, it becomes more difficult for these variations to exist, which may account for the well-known Maunder minimum of solar activity.

Modeling the rotation of the flat subsystem and determining the distance to the center of the galaxy: Realistic quality of the model and optimization of its complexity

Unrealistic assumptions about the law of Galactic rotation in kinematic methods of determining the distance to the center of the Galaxy (R 0) can strongly distort the result. An empirical method for optimizing the smoothness of the model rotation curve is proposed that eliminates the corresponding systematic errors in R0. A generalized procedure for estimating R0from an analysis of the rotation of an arbitrary, uniform, flat subsystem of Galactic objects is developed.

Non-axisymmetric solar magnetic fields

A simple non-linear, non-axisymmetric mean field dynamo model is applied to a differentially rotating spherical shell. Two approximations are used for the angular velocity, to represent what is now believed to be the solar rotation law. In each case, stable solutions are found which possess a small non-axisymmetric field component. Although the model has a number of obvious shortcomings, it may be relevant to the problem of the solar active longitudes.

Radiation Hydrodynamical Mass Accretion onto Galactic Nuclei Driven by Circumnuclear Starbursts

Abstract We explore the radiation hydrodynamical evolution of a galactic nuclear gas disk exposed to intense radiation from circumnuclear starbursts. The evolution is characterized by two stages. First, the disk is radially contracted by the radiation force. Subsequently, the surface stratum of the disk avalanches onto the center due to the removal of angular momenta by radiation drag. The mass accretion via a radiatively-driven avalanche was analyzed quantitatively while assuming a torus shape of the circumnuclear starburst regions. As a result, it was found that the mass-accretion rate is sensitively dependent upon the extension of the starburst regions. For an optically thick disk, the mass-accretion rate is roughly in proportion to the ratio of the thickness to the curvature radius of the torus. The rate is also dependent upon the rotation law of the disk. We investigated the evolution of the disk surface density resulting from radiatively-driven mass accretion. It was found that for a more intensive starburst the central concentration of surface density becomes more conspicuous. The present results seem to be significant when considering the evolution of starburst nuclei, for instance, in luminous IRAS galaxies.

The non-linear fluid dynamics of a warped accretion disc

The dynamics of a viscous accretion disc subject to a slowly varying warp of large amplitude is considered. Attention is restricted to discs in which self-gravitation is negligible, and to the generic case in which the resonant wave propagation found in inviscid Keplerian discs does not occur. The equations of fluid dynamics are derived in a coordinate system that follows the principal warping motion of the disc. They are reduced using asymptotic methods for thin discs, and solved to extract the equation governing the warp. In general, this is a wave equation of parabolic type with non-linear dispersion and diffusion, which describes fully non-linear bending waves. This method generalizes the linear theory of Papaloizou & Pringle (1983) to allow for an arbitrary rotation law, and extends it into the non-linear domain, where it connects with a generalized version of the theory of Pringle (1992). The astrophysical implications of this analysis are discussed briefly.

The Taylor‐Proudman Balance and the Solar Rotational Data

For the Sun (and because of the presence of buoyancy), the implications of the Taylor-Proudman balance (TPB, a balance between the pressure, Coriolis, and buoyancy forces in the radial and latitudinal momentum equations) differ fundamentally from those of an incompressible fluid. The TPB now only determines the latitudinal variations of the solar entropy in terms of the rotation law and known functions of r. As a consequence of the TPB, the energy equation is in fact an equation for the angular velocity, Ω(r, θ)=Ω0(ω0(r)+ω2(r)P2(cos θ)), where P2(cos θ) is the second-order Legendre polynomial. In agreement with data from the Solar Oscillations Investigations project (SOI) Michelson Doppler Imager (MDI) on board SOHO, we assume that ω0(r) is constant with r, and solve the equation for ω2(r) with a simple, heuristic expression for the convective flux [if ω0(r) is constant, then ∂Ω/∂r vanishes for θc=547, P2(cos θc)=0, in remarkable agreement with Kosovichev's results inferred from isocontours for Ω(r, θ)]. For values of the meridional motions that are not too large, solutions for ω2(r) exist that agree with these isocontours. These solutions are such that the latitudinal variation of the convective flux, arising from the latitudinal variations of the entropy, required by the TPB, are significantly reduced.

Solar torsional oscillations and the grand activity cycle

Some consequences of a nonlinear coupling between magnetic field and rotation are studied within a solar type 2D dynamo model for a spherical convective shell. The magnetic feedback on the rotation law produces two main effects. First, the torsional oscillations are excited. Second, a long-term amplitude modulation of the dynamo cycles is produced. The latter may be identified with the grand cycle of solar activity. The dynamo model seems to be in accord with the phase relations between the torsional and magnetic activity oscillations observed in the 11-year cycle as well as in the 55-year grand cycle. It, however, fails to reproduce the observationally suggested global decreasing trend in the equatorial rotation rate.

Viscosity alpha in rotating spherical shear flows with an external magnetic field

We study the turbulent behaviour induced by the magnetic shear instability for a magnetized, incompressible fluid in a spherical shell. A differential rotation that is decreasing outwards but hydrodynamically stable according to the Rayleigh criterion is prescribed, and an external, uniform magnetic field is imposed parallel to the rotation axis. Our main concern in this paper is the fully global treatment of this magnetohydrodynamical system, so we focus particular attention on the influence of the boundary conditions. Non-linear, steady solutions are presented for stress-free as well as for rigid boundary conditions for one specific model with a fixed strength of the external magnetic field and a fixed differential rotation rate. We calculate the eddy viscosity νT and the viscosity alpha αSS resulting from the total stress tensor. These turbulence parameters turn out to differ drastically depending on the boundary conditions for the flow. An investigation of the radial structure of the viscosity alpha (whilst varying the differential rotation law) shows that the enhanced generation of turbulence takes place mainly in the boundary layers of the shell.

Viscosity alpha in rotating spherical shear flows with an external magnetic field

We study the turbulent behaviour induced by the magnetic shear instability for a magnetized, incompressible fluid in a spherical shell. A differential rotation that is decreasing outwards but hydrodynamically stable according to the Rayleigh criterion is prescribed, and an external, uniform magnetic field is imposed parallel to the rotation axis. Our main concern in this paper is the fully global treatment of this magnetohydrodynamical system, so we focus particular attention on the influence of the boundary conditions. Non-linear, steady solutions are presented for stress-free as well as for rigid boundary conditions for one specific model with a fixed strength of the external magnetic field and a fixed differential rotation rate. We calculate the eddy viscosity νT and the viscosity alpha αSS resulting from the total stress tensor. These turbulence parameters turn out to differ drastically depending on the boundary conditions for the flow. An investigation of the radial structure of the viscosity alpha (whilst varying the differential rotation law) shows that the enhanced generation of turbulence takes place mainly in the boundary layers of the shell.

Stellar Evolution with Arbitrary Rotation Laws. III. Convective Core Overshoot and Angular Momentum Distribution

Intermingled two-dimensional hydrodynamic and two-dimensional stellar evolution calculations are presented for two 8.75 M☉ models, one nonrotating and one rotating with a zero-age main sequence surface equatorial rotational velocity of 200 km s-1. The first calculation of the rotating model was made assuming no convective core overshooting and enforcing solid-body rotation in the convective core. Hydrodynamic simulations at various stages of core hydrogen burning indicate that neither of these assumptions is true. Overshooting to a distance equivalent to about 0.35 pressure scale heights is found, and there is some evidence that the distance in terms of the pressure scale height increases slightly in later stages of core hydrogen burning. This is not a claim that the pressure scale height is a relevant parameter for determining overshooting distances. The dynamic calculations also show that the rotation rate in the convective core is approximately constant on cylinders and that the rate may be expressed as a power law in the distance from the rotation axis, as long as there is a cutoff at small distances. Two more evolutionary sequences, one rotating and one not, were calculated utilizing these results. The largest effects are produced from the overshooting and are esssentially those found by previous researchers. However, the angular momentum distribution in the interior at the end of core hydrogen burning is significantly different for this second case than for the one assuming solid-body rotation in the convective core. The primary differences are that the horizontal variation in the rotation rate is much larger and that the rotation rate near the center is much higher in the second case.

Magnetic and vertical shear instabilities in accretion discs

ABSTRA C T The stability properties of magnetized discs rotating with angular velocity Q o Q﷿s; zfi, dependent on both the radial and the vertical coordinates s and z, are considered. Such a rotation law is adequate for many astrophysical discs (e.g., galactic and protoplanetary discs, as well as accretion discs in binaries). In general, the angular velocity depends on height, even in thin accretion discs. A linear stability analysis is performed in the Boussinesq approximation, and the dispersion relation is obtained for short-wavelength perturbations. Any dependence of Q on z can destabilize the flow. This concerns primarily small-scale perturbations for which the stabilizing effect of buoyancy is strongly suppressed due to the energy exchange with the surrounding plasma. For a weak magnetic field, instability of discs is mainly associated with vertical shear, whilst for an intermediate magnetic field the magnetic shear instability, first considered by Chandrasekhar and Velikhov, is more efficient. This instability is caused by the radial shear which is typically much stronger than the vertical shear. Therefore the growth time for the magnetic shear instability is much shorter than for the vertical shear instability. A relatively strong magnetic field can suppress both these instabilities. The vertical shear instability could be the source of turbulence in protoplanetary discs, where the conductivity is low.

Viscous and rotational splitting of the translational oscillations of Earth's solid inner core

The small oscillations of the inner core about its central position present an interesting problem in fluid dynamics with roots in the classical literature. It is a generalization of the problem Stokes [Stokes, G.G., 1851. On the effect of the internal friction of fluids on the motion of pendulums, Trans. Cambridge Philos. Soc. 9, 8.] solved of a sphere oscillating in an unbounded, non-rotating, viscous fluid to the case of a sphere oscillating in the contained, rotating fluid outer core. In the inviscid case, the influence of the Coriolis acceleration splits the oscillation into three distinct motions with differing periods, one along the axis of rotation, one prograde in the equatorial plane, and one retrograde in the equatorial plane. In this paper, we consider the effect of the presumed high viscosity at the inner core boundary on the rotational splitting. We obtain novel exterior analytic solutions of the Poincaré equation for the flow outside the boundary and solve the Ekman boundary-layer problem to match the no-slip condition at the inner core boundary. Continuity of normal displacement at the inner core boundary, and in far-field approximation at the core–mantle boundary, determine the free constants in the two independent Poincaré solutions. Conservation of linear momentum between the inner core, outer core and shell establishes a centre of mass reference frame. Analytic expressions for the pressure and viscous drag are obtained for both the axial and equatorial modes of oscillation. These are then used in the equation of motion for the inner core to deduce viscous and rotational splitting laws. Viscosity is found to reduce the effect of rotation on the periods of all three modes; most noticeably, it reduces the large rotational splitting of the two equatorial modes. We expect the geophysically interesting value of the viscosity just outside the inner core might be recovered from the observed splitting, particularly, that of the two equatorial modes.

Differential Rotation and Meridional Flow for Fast‐rotating Solar‐Type Stars

Observations indicate that normalized surface differential rotation decreases for fast-rotating stars, that is, | ΔΩ |/Ω ∝ Ω-0.3. An increase of | ΔΩ |/Ω is provided, however, by the current Reynolds stress theory of differential rotation in stellar convection zones, without the inclusion of meridional flow. We compute both the pole-equator difference of the surface angular velocity and the meridional drift for various Taylor numbers to demonstrate that the inclusion of meridional flow in the computations for fast rotation yields a systematic reduction of the resulting differential rotation. Our model's adiabatic and density-stratified convection zone, with stress-free surfaces and a thickness of 0.3 stellar radii, yields the relation | ΔΩ |/Ω ∝ Ω-(0.15 ... 0.30) for stars with faster rotation than the Sun, in agreement with previous observations. If the Coriolis number rather than the Taylor number is varied, we find a maximum differential rotation of 20%. For stars with fast rotation, exponents of up to n' 0.4 are found. All rotation laws exhibit superrotating equators.

MrK86: A 'Not-So-Dark' Galaxy

We have studied the velocity field of the Blue Compact Dwarf galaxy Mrk86 using an Hα Fabry-Perot image and 14 long-slit optical spectra. From the ionized gas velocities measured we have found that Mrk86 follows a solid-body rotation law with a central angular velocity of 34 ± 5 km s-1 kpc-1. The comparison of the modeled rotation curve with our velocity data indicates a clear dominance of the stellar mass component over the dark matter. Related with the galaxy most intense star forming knot, a very strong gradient steeping is observed. Finally, we give kinematic evidence for the Mrk86-C expanding bubble.

Three‐dimensional Simulations of Runaway Instability of Self‐gravitating Accretion Disks

Runaway instability of accretion disks around black holes, i.e., unstable mass overflow from disks to black holes, has been investigated by computing the time evolution of self-gravitating disks. It is crucial to include self-gravity of the disk in numerical simulations because it has been shown that self-gravity of the disk is the main cause of the instability. Dynamical evolutions of self-gravitating disks with several representative rotation laws, i.e., constant specific angular momentum disks, Kepler-type disks, and constant linear velocity disks, have been pursued by using the smoothed particle hydrodynamics code with 12,000 pseudoparticles. We have found that if the ratio of the disk mass to the black hole mass exceeds about 10-1.8, self-gravitating disks suffer from runaway instability and that the matter of the disks flows down to the central black hole in 1-2 times the dynamical timescale. This is common to almost all models irrespective of rotation laws.

The dependence of the dynamo alpha on vorticity

We use data from numerical simulations of dynamo-generated turbulence in the shearing box approximation to determine the dynamo a-effect and its dependence on the rotation law O(r). The data suggest that the dynamo a is not simply proportional to the local angular velocity O(r), as is usually assumed, but rather is proportional to the local vorticity w(r) = r-1d/dr(Or 2 ). We also find tentative evidence to support the proposition that the backreaction of the magnetic field on a sets in when the field reaches equipartition with the energy in the turbulent motions. Furthermore, we propose an explanation as to why the sign of a is found to be opposite to that in the standard picture.

How things work: the physics of everyday life

How things work: the physics of everyday life