Differential Rotation Pattern Research Articles

Glitches induced by the core superfluid in a neutron star

The long-term evolution of the relative rotation of the core superfluid in a neutron star with respect to the rest of the star, at different radial distances from the rotation axis, is determined through model calculations. The core superfluid rotates at a different rate (faster, in young pulsars), while spinning down at the same steady-state rate as the rest of the star, because of the assumed pinning between the superfluid vortices and the superconductor fluxoids. We find that the magnitude of this rotational lag changes with time and also depends on the distance from the rotation axis; the core superfluid supports an evolving pattern of differential rotation. We argue that the predicted change of the lag might occur as discrete events which could result in a sudden rise of the spin frequency of the crust of a neutron star, as is observed at glitches in radio pulsars. This new possibility for the triggering cause of glitches in radio pulsars is further supported by an estimate of the total predicted excess angular momentum reservoir of the core superfluid. The model seems to offer also resolutions for some other aspects of the observational data on glitches.

Doppler Imaging of Stars with Surface Inhomogeneities

AbstractI review recent progress in the field of stellar surface imaging, with particular reference to advanced methods for mapping surface-brightness distributions on magnetically active late-type stars. New signal enhancement techniques, utilising profile information from hundreds or thousands of photospheric lines simultaneously, allow images to be derived for stars several magnitudes fainter than was previously possible. For brighter stars, the same techniques make it possible to map features as small as two or three degrees in extent on the stellar surface. While this opens up whole new areas of research, such as the ability to use starspot tracking to study surface differential rotation patterns on single and binary stars, caution must be exercised in the treatment of “nuisance” parameters such as the stellar rotation rate, surface abundances and radial velocity. At the very high S:N levels we now use, the effects of systematic errors in these parameters are easier to identify, isolate and eliminate. This leads to the possibility of making precise radial velocity variations (at the few hundred m s−2 level or better) in late-type stars even with equatorial rotation speeds as high as 100 km s−1. This is particularly topical given the recent discovery that one of our prime imaging targets, the young southern K0 dwarf AB Doradus, has an astrometric companion in a highly eccentric orbit with an inferred mass close to the H-burning limit.

Far‐Infrared [C ii ] Line Survey Observations of the Galactic Plane

We present results of our survey observations of the [C II] 158 μm line emission from the Galactic plane using the Balloon-borne Infrared Carbon Explorer (BICE). Our survey covers a wide area (350° l 25°, |b| 3°) with a spatial resolution of 15'. We employed a new observing method called fast spectral scanning to make large-scale observations efficiently. Strong [C II] line emission was detected from almost all areas we observed. In the general Galactic plane, the spatial distribution of the [C II] line emission correlates very well with that of far-infrared continuum emission, but diffuse components are more prominent in the [C II] line emission; the I[C II]/IFIR ratio is ~0.6% for diffuse components but is ~0.2% for compact sources such as active star-forming regions. In the Galactic center region, on the other hand, the distribution of the [C II] line emission is quite different from that of the far-infrared continuum emission, and the I[C II]/IFIR ratio is systematically lower there. The FWHM velocity resolution of our instrument is 175 km s-1, but we determined the central velocity of the line at each observed point very precisely with statistical errors as small as ±6 km s-1. The longitudinal distribution of the central velocity clearly shows the differential rotation pattern of the Galactic disk and also violent velocity fields around the Galactic center.

Numerical simulations of thermal convection in a rotating spherical fluid shell at high Taylor and Rayleigh numbers

In this study, we carry out numerical simulations of thermal convection in a rapidly rotating spherical fluid shell at high Taylor number Ta and Rayleigh number R with a nonlinear, three-dimensional, time-dependent, spectral-transform code. The parameters used in the simulations are chosen to be in a range which allows us to study two different types of convection, i.e., single column and multi-layered types, and the transition between them. Numerical solutions feature highly time-dependent north–south open columnar convective cells. The cells occur irregularly in longitude, are quasi-layered in cylindrical radius, and maintain alternating bands of mean zonal flow. The complex convective structure and the banded mean zonal flow are results of the high Taylor and Rayleigh numbers. The transition between the two types of convection appears to occur gradually with increasing Rayleigh and Taylor numbers. At a Taylor number of 107 the differential rotation pattern consists of an inner cylindrical region of subrotation and an outer cylindrical shell of superrotation manifest at the outer boundary as an equatorial superrotation and a high latitude subrotation. The differential rotation pattern is similar at Ta=108 and low Rayleigh number. Cylindrical shells of alternately directed mean zonal flow begin to develop at Ta=108 and R=50Rc and at Ta=109 and R=25Rc. This pattern is seen on the outer surface as a latitudinally-banded zonal flow consisting of an equatorial superrotation, a middle and high latitude subrotation, and a polar superrotation. At Ta=109 and R=50Rc the differential rotation appears at the surface as a broad eastward flow in the equatorial region with alternating bands of westward and eastward flow at high latitudes.

Transitions to chaotic thermal convection in a rapidly rotating spherical fluid shell

Abstract Numerical simulations of thermal convection in a rapidly rotating spherical fluid shell heated from below and within have been carried out with a nonlinear, three-dimensional, time-dependent pseudospectral code. The investigated phenomena include the sequence of transitions to chaos and the differential mean zonal rotation. At the fixed Taylor number T a =106 and Prandtl number Pr=1 and with increasing Rayleigh number R, convection undergoes a series of bifurcations from onset of steadily propagating motions SP at R=R c = 13050, to a periodic state P, and thence to a quasi-periodic state QP and a non-periodic or chaotic state NP. Examples of SP, P, QP, and NP solutions are obtained at R = 1.3R c , R = 1.7 R c , R = 2R c , and R = 5 R c , respectively. In the SP state, convection rolls propagate at a constant longitudinal phase velocity that is slower than that obtained from the linear calculation at the onset of instability. The P state, characterized by a single frequency and its harmonics, has a two-layer cellular structure in radius. Convection rolls near the upper and lower surfaces of the spherical shell both propagate in a prograde sense with respect to the rotation of the reference frame. The outer convection rolls propagate faster than those near the inner shell. The physical mechanism responsible for the time-periodic oscillations is the differential shear of the convection cells due to the mean zonal flow. Meridional transport of zonal momentum by the convection cells in turn supports the mean zonal differential rotation. In the QP state, the longitudinal wave number m of the convection pattern oscillates among m = 3,4,5, and 6; the convection pattern near the outer shell has larger m than that near the inner shell. Radial motions are very weak in the polar regions. The convection pattern also shifts in m for the NP state at R = 5R c , whose power spectrum is characterized by broadened peaks and broadband background noise. The convection pattern near the outer shell propagates prograde, while the pattern near the inner shell propagates retrograde with respect to the basic rotation. Convection cells exist in polar regions. There is a large variation in the vigor of individual convection cells. An example of a more vigorously convecting chaotic state is obtained at R = 50R c . At this Rayleigh number some of the convection rolls have axes perpendicular to the axis of the basic rotation, indicating a partial relaxation of the rotational constraint. There are strong convective motions in the polar regions. The longitudinally averaged mean zonal flow has an equatorial superrotation and a high latitude subrotation for all cases except R = 50R c , at this highest Rayleigh number, the mean zonal flow pattern is completely reversed, opposite to the solar differential rotation pattern.

Depth and latitude dependence of the solar internal angular velocity

One of the design goals for the dedicated helioseismology observing state located at Mount Wilson Observatory was the measurement of the internal solar rotation using solar p-mode oscillations. In this paper, the first p-mode splittings obtained from Mount Wilson are reported and compared with those from several previously published studies. It is demonstrated that the present splittings agree quite well with composite frequency splittings obtained from the comparisons. The splittings suggest that the angular velocity in the solar equatorial plane is a function of depth below the photosphere. The latitudinal differential rotation pattern visible at the surface appears to persist at least throughout the solar convection zone.

The Solar Gravitational Figure - j2 and J4

The theory of the solar gravitational figure is derived including the effects of differential rotation. It is shown that J sub 4 is smaller than J sub 2 by a factor of about 10 rather than being of order J sub 2 squared as would be expected for rigid rotation. The dependence of both J sub 2 and J sub 4 on envelope mass is given. High order p-mode oscillation frequencies provide a constraint on solar structure which limits the range in envelope mass to the range 0.01 M sub E/solar mass 0.04. For an assumed rotation law in which the surface pattern of differential rotation extends uniformly throughout the convective envelope, this structural constraint limits the ranges of J sub 2 and J sub 4 in units of 10 to the -8th power to 10 J sub 2 15 and 0.6 -J sub 4 1.5. Deviations from these ranges would imply that the rotation law is not constant with depth and would provide a measure of this rotation law.