Limb Shift Research Articles

Characterizing Solar Surface Convection Using Doppler Measurements

Abstract The Helioseismic Magnetic Imager on board the Solar Dynamics Observatory records line-of-sight Dopplergram images of convective flows on the surface. These images are used to obtain the multiscale convective spectrum. We design a pipeline to process the raw images to remove large-scale features like differential rotation, meridional circulation, limb shift, and imaging artifacts. The Hierarchical Equal Area Pixelization scheme is used to perform spherical harmonic transforms on the cleaned image. Because we only have access to line-of-sight velocities on half the solar surface, we define a “mixing matrix” to relate the observed and true spectra. This enables the inference of poloidal and toroidal flow spectra in a single step through the inversion of the mixing matrix. Performing inversions on a number of flow profiles, we find that the poloidal flow recovery is most reliable among all the components. We also find that the poloidal spectrum is in qualitative agreement with inferences from Local Correlation Tracking of granules. The fraction of power in vertical motions increases as a function of wavenumber and is at the 8% level for ℓ = 1500. In contrast to seismic results and LCT, the flows show nearly no temporal-frequency dependence. Poloidal flow power peaks in the range of ℓ − ∣m∣ ≈ 150–250, which may potentially hint at a latitudinal preference for convective flows.

Attitude Sensor from Ellipsoid Observations: A Numerical and Experimental Validation.

The preliminary design and validation of a novel, high accuracy horizon-sensor for small satellites is presented, which is based on the theory of attitude determination from ellipsoid observations. The concept consists of a multi-head infrared sensor capturing images of the Earth limb. By fitting an ellipse to the imaged limb arcs, and exploiting some analytical results available from projective geometry, a closed form solution for computing the attitude matrix is provided. The algorithm is developed in a dimensionless framework, requiring the knowledge of the shape of the imaged target, but not of its size. As a result, the solution is less sensitive to the limb shift caused by the atmospheric own radiance. To evaluate the performance of the proposed method, a numerical simulator is developed, which generates images captured in low Earth orbit, including also the presence of the atmosphere. In addition, experimental validation is provided due to a dedicated testbed, making use of a miniature infrared camera. Results show that our sensor concept returns rms errors of few hundredths of a degree or less in determining the local nadir direction.

The direction of force twitches evoked by TMS in a passive limb shift according to the direction of impending contralateral muscle activation

The direction of force twitches evoked by TMS in a passive limb shift according to the direction of impending contralateral muscle activation

VARIABILITY OF SURFACE FLOWS ON THE SUN AND THE IMPLICATIONS FOR EXOPLANET DETECTION

The published Mount Wilson Doppler-shift measurements of the solar velocity field taken in 1967--1982 are revisited with a more accurate model, which includes two terms representing the meridional flow and three terms corresponding to the convective limb shift. Integration of the recomputed data over the visible hemisphere reveals significant variability of the net radial velocity at characteristic time scales of 0.1--10 years, with a standard deviation of 1.4 \ms. This result is supported by independent published observations. The implications for exoplanet detection include reduced sensitivity of the Doppler method to Earth-like planets in the habitable zone, and an elevated probability of false detections at periods of a few to several years.

Development of “Normal” Dermatomes and Somatotopic Maps by “Abnormal” Populations of Cutaneous Neurons

During development, motor and sensory axons grow to peripheral targets with remarkable precision. Whereas much has been learned about the development of motoneuron connectivity, less is known about the regulation of cutaneous innervation. In adults, dorsal root ganglia (DRG) innervate characteristic skin regions, termed dermatomes, and their axons project somatotopically in the dorsal horn. Here, we have investigated whether cutaneous neurons are selectively matched with specific skin regions, and whether peripheral target skin influences the central connections of cutaneous neurons. To address these questions, we shifted limb buds rostrally in chick embryos prior to axon outgrowth, causing DRGs to innervate novel skin regions, and mapped the resulting dermatomes and central projections. Following limb shifts, cutaneous innervation arose from more rostral and from fewer DRGs than normal, but the overall dermatome pattern was preserved. Thus, DRGs parcel out innervation of skin in a consistent manner, with no indication of matching between skin and DRGs. Similarly, cutaneous nerves established a “normal” somatotopic map in the dorsal horn, but in more rostral segments than usual. Thus, the peripheral target skin may influence the pattern of CNS projections, but does not direct cutaneous axons to specific populations of neurons in the dorsal horn.

Independent Development of Sensory and Motor Innervation Patterns in Embryonic Chick Hindlimbs

Previous studies suggest that sensory axon outgrowth is guided by motoneurons, which are specified to innervate particular target muscles. Here we present evidence that questions this conclusion. We have used a new approach to assess the pathfinding abilities of bona fide sensory neurons, first by eliminating motoneurons after neural crest cells have coalesced into dorsal root ganglia (DRG) and second by challenging sensory neurons to innervate muscles in a novel environment created by shifting a limb bud rostrally. The resulting sensory innervation patterns mapped with the lipophilic dyes DiI and DiA showed that sensory axons projected robustly to muscles in the absence of motoneurons, if motoneurons were eliminated after DRG formation. Moreover, sensory neurons projected appropriately to their usual target muscles under these conditions. In contrast, following limb shifts, muscle sensory innervation was often derived from inappropriate segments. In this novel environment, sensory neurons tended to make more “mistakes” than motoneurons. Whereas motoneurons tended to innervate their embryologically correct muscles, sensory innervation was more widespread and was generally from more rostral segments than normal. Similar results were obtained when motoneurons were eliminated in embryos with limb shifts. These findings show that sensory neurons are capable of navigating through their usual terrain without guidance from motor axons. However, unlike motor axons, sensory axons do not appear to actively seek out appropriate target muscles when confronted with a novel terrain. These findings suggest that sensory neuron identity with regard to pathway and target choice may be unspecified or quite plastic at the time of initial axon outgrowth.

Peering over the Sun's pole: behavior of its rotational vortex

A new method for measuring spectroscopically the rotation at the Sun's poles is described. Using solar CO lines at 4.666 µm, infrared spectra are recorded at a fixed limb distance of 4.8 arc sec while progressing along an arc ±5.7 deg from the Sun's rotational pole. Since the poles dip twice a year to about 7 arc sec from the limb, our observations can range either side of and through the vortex axis. Advantages to this technique are: (1) a low disturbing signal from supergranules owing to their superposition at the limb, (2) no ‘limb shift’ error since limb distance is constant and the CO lines have no known limb shift, (3) emphasis is on the quiet Sun since the CO molecule is confined there, (4) negligible scattered light in the IR (<1%), and (5) the improved seeing afforded by the IR. Although any definitive determination of solar rotation requires observations over an extended time span, our preliminary results suggest two features peculiar to the extreme pole: (1) the occasional apparent cessation of rotation, (2) some sort of singularity, again occasional, producing a sharp velocity signal (a vortex?) within 1 deg of the pole.

Skin sensory innervation patterns in embryonic chick hindlimbs deprived of motoneurons

During normal development and following a variety of experimental manipulations (e.g., neural tube rotations, limb shifts), sensory neurons in the chick grow to their correct targets. L. Landmesser and M. G. Honig (1986, Dev. Biol. 118, 511–531) have suggested that sensory innervation may be precise, not because sensory neurons respond to limb-derived guidance cues, but because sensory neurons interact with motoneurons, which do respond to such cues. To test this hypothesis for skin sensory neurons, the ventral neural tube, including the motoneuron precursors, was removed from chick embryos prior to sensory axon outgrowth and the resulting patterns of dermatomes and axonal projections were mapped physiologically and anatomically. As reported previously, dorsal root ganglia (DRGs) and cutaneous nerves formed in their usual locations following the early removal of motoneurons, while most muscle nerves and the plexus region were reduced substantially (A. C. Taylor, 1944, J. Exp. Zool. 96, 159–185 ; L. Landmesser and M. G. Honig, 1986, Dev. Biol. 118, 511–531 ; G. J. Swanson and J. Lewis, 1986, J. Embryol. Exp. Morphol. 95, 37–52) . The patterns of axonal projections and dermatomes were surprisingly, although not entirely, normal. In particular, cutaneous nerves in motoneuron-depleted embryos were derived from the same DRGs in approximately the same proportions as normal. Thus, while motoneurons may play a facilitative role in the development of the segmental pattern of skin sensory innervation, they do not appear to be essential.

Solar rotation measurements at Mount Wilson

The procedure for reducing the data acquired during the Mt. Wilson Observatory synoptic program is described, and a program for acquiring as many scans per day as possible of the solar magnetic and velocity fields is discussed. A fitting formula which removes the background velocity field from each scan has been derived. It is suggested that the difference between the limb shift along the north-south axis and the east-west axis may be due to the meridional circulation.

Variations in the mean line of sight velocity of the Sun: 1976–1985

Measurements of the line of sight velocity of the sun with respect to earth have been obtained at Izaña (Tenerife) during the years 1976 to 1985. The mean values found for each year show a trend of ~30 m/s from minimum to maximum. Their mean value is of 583.1 ± .2 m/s which is 92% of the gravitational red shift predicted by theory and their variation seems to be related to the solar cycle with the clear exception of 1985. The most likely interpretation is that the velocity limb shift effect, averaged over the whole sun, is the cause of the slight disagreement with theory and this effect changes with time.

Simulating photospheric Doppler velocity fields

A method is described for constructing artificial data that realistically simulate photospheric velocity fields. The velocity fields include rotation, differential rotation, meridional circulation, giant cell convection, supergranulation, convective limb shift, p-mode oscillations, and observer motion. Data constructed by this method can be used for testing algorithms designed to extract and analyze these velocity fields in real Doppler velocity data.

Distribution of fiber types in embryonic chick limb muscles innervated by foreign motoneurons

The differentiation of distinct myotube fiber types in chick limb muscle development is coincident with innervation. The role of motoneurons in influencing fiber type differentiation was analyzed by causing chick hind limb muscles to be innervated by inappropriate motoneurons and then examining experimental muscles for changes in the distribution of myosin ATPase fiber types. Motoneuron innervation of limb muscles was altered by performing either limb shifts, limb reversals, or large spinal cord reversals on early neural tube or limb bud stage chick embryos. The distribution of fiber types was then analyzed in muscles from stage 36 (E10) to stage 45 (E20) embryos after processing hind limb sections for myosin ATPase histochemistry. In the majority of experimental muscles examined ( 267 312 ), the distribution of myosin ATPase fiber types was unaltered. In the remaining experimental muscles (14%), alterations in the distribution of myosin ATPase fiber types occurred, indicating that in some cases, foreign innervation may alter the developmental program of differentiating myotubes. The results suggest that myotubes differentiate myosin ATPase staining characteristics according to an intrinsic program and that these differentiating myotubes are selectively innervated by motoneurons of the appropriate type under most conditions including normal development. Under exceptional circumstances of motoneuron-muscle fiber type mismatch, embryonic motoneurons can alter fiber type expression.

Spherical harmonic analysis of steady photospheric flows

Steady photospheric flows can be represented by a spectrum of spherical harmonic modes. A technique is described in which full disc doppler velocity measurements are analysed using the spherical harmonic functions to determine the characteristics of this spectrum and the nature of these flows. Synthetic data is constructed for testing this technique. This data contains limb shift, rotation, differential rotation, meridional circulation, supergranules, giant cells and various levels of noise. The data is analysed in several steps. First, the limb shift is calculated by finding the average velocity in concentric rings about disc center. A polynomial representation of the limb shift is then removed from the data. Secondly, the rotation profile is calculated by finding an average slope in the velocity across the disc at each latitude position. This rotation profile is fit with Legendre polynomials and removed from the data. The third step is to find the meridional circulation by calculating the spherical harmonic transform for the axisymmetric poloidal modes and correcting for the effects of the limb shift analysis. The final step is to calculate the full spectrum of spherical harmonic components for the convective flows. Supergranules are separated from giant cells by spectral filtering for high (l >32) and low (l <32) wavenumbers, respectively. Some information about the spectrum is lost because only one hemisphere is seen, only the line-of-sight velocity is measured and the measurements contain noise. The lack of information about the motions on the backside of the Sun produces a broad smearing of the spectrum into nearby modes. The lack of information about the transverse velocity component produces a mixing between modes whose longitudinal wavenumbers differ by two and between the poloidal and toroidal components with the same wavenumber. In spite of this mode mixing much can be learned from this analysis. Solar rotation and differential rotation can be accurately measured and monitored for secular changes. Meridional circulations with small amplitudes can be measured and monitored and giant cells can be separated from supergranules.

The radial velocity of the sun as a star and the solar cycle

Radial velocity measurements of the sun as a star using a resonant scattering spectrometer have been obtained at Izaña (Tenerife) during long observing seasons from 1976 to 1985. Its analysis shows that except for the global oscillations with periods shorter than one day there are stable signals with longer periods: at ∼13 days with mean amplitude of ∼ 3 m/s (it changes with the solar cycle) and another one of ∼ 15 m/s amplitude which shows a temporal variation of various years related to the solar cycle. The first signal has a partial explanation as an effect produced by the passage of active regions through the visible surface of the sun but it does not completely explain the observed signal. The second one, related to the limb shift, is probably due to changes in the convection zone in connection with the solar cycle.

Limits on photospheric Doppler signatures for solar giant cells

Mount Wilson solar-velocity data taken since improvement of the spectrograph in May 1982 are analyzed to search for photospheric traces of persistent velocity patterns that are anticipated in recent model predictions. The method involves time-averaged autocorrelations and cross correlations of the residuals that remain after least-squares fits for differential rotation, limb shift, and meridional circulation are extracted from the daily-magnetogram velocity arrays. It is argued that, owing to the supergranular motions in the photosphere, the sensitivity in applying the present method to the new Mount Wilson data is close to the ultimate sensitivity possible for detection of this phenomenon. The following limits are currently established through this analysis: (1) there is no sharply peaked power spectrum with amplitude above about 1 m/s per wavenumber, and (2) there is no broad-band power spectrum for which the total integrated power is greater than about 10 sq m/sq sec.

Plasma motion in umbrae and the surrounding photosphere derived from spectroscopic Doppler measurements and tracer measurements of spots

The rotational velocity of the Sun is determined by sunspot tracings and by spectroscopic measurements of the photospheric plasma using the non-Zeeman-split line Fe i 5576 and absolute iodine reference. Stationary line shifts as limb-effect and longperiodical shifts introduced by supergranulation are discussed. The dependence on solar activity as Ca+ emissivity and magnetic fields is investigated including line asymmetries. The results are: (a) The non active photospheric regions rotate with 1995 ± 30 m s-1. Solar active regions yield a 60 m s-1 higher value. (b) In quiet regions the absolute limb shift varies between 170 m s-1 at the line core and 310 m s-1 at I/I cont ≈ 0.8 (C-shape); thus the limb shift is mainly due to entire line shifts. (c) In solar active regions (close to spots) asymmetries are widely reduced in line cores; this effect cannot be associated with a variation of the limb effect due to a large scatter of Doppler shifts near spots. (d) A reduced limb shift of 50 m s-1 is found in network boundaries and is mainly due to a small scale downflow. (e) Observations with a smaller influence of stray light yield symmetric profiles in umbrae. (f) Differences between umbral rotation rates from tracer and spectroscopic measurements do not exceed 20 m s-1, when considering straylight. The rotational velocity from umbrae exceeds that from the photosphere by 30–60 m s-1. Some individual spots yield nearly the same rotation rate as the photosphere.

Pathway selection by embryonic chick motoneurons in an experimentally altered environment.

To characterize cues used by motoneuron axons to reach their appropriate targets, connectivity patterns within the embryonic chick hindlimb have been analysed after early experimental manipulations of the limb or spinal cord. The manipulations altered the anterior-posterior (a.-p.) relationship between motoneurons within the lumbosacral motor column and their specific targets in the limb. Primary emphasis was placed on analysing the pathways taken by embryonic motoneuron axons at stages 23-36 which had been orthogradely labelled by horseradish peroxidase (HRP) injection into the motor column. Motoneuron pool topography and functional patterns of connectivity were also identified by retrograde HRP labelling and spinal cord stimulation coupled with electromyographic recording. With small shifts in position, as in two or three segment a.-p. cord reversals or a.-p. limb shifts, motoneuron axons frequently entered the appropriate plexus but in an inappropriate spinal nerve sequence. Despite this, axons altered their course to innervate specifically and consistently their current target. When motoneuron axons entered an inappropriate plexus as the result of a greater positional shift (i.e. more extensive cord reversal or limb shift) or in experiments where posterior cord segments were replaced with anterior cord segments and supernumerary limbs were added, they behaved in one of two ways. They either formed inappropriate and largely unpatterned or unordered connections or they took totally aberrant paths within the limb to reach their appropriate target. We conclude that axons are capable of responding in a precise and specific manner to environmental cues when displaced up to a certain distance from their target or normal point of entry into the limb. Their failure to form patterned connections at more extreme distances suggests that the cues to which they are responding may be local, or that an axon's ability to respond to them is restricted to subclasses of the motoneuron population.

Some comments on the limb shift of solar lines

We searched for a variation with heliographic latitude of the solar limb effect by comparing the relative wavelengths of weak and strong Fraunhofer lines. The blue shifts associated with the limb effect appear 9%±5% larger in the polar radius vector than in an equatorial radius vector at cos θ = 0.5. This should perhaps be interpreted as an increase with latitude of either solar convection or of convective overshoot. Recent observations of poleward meridional flows of 30m s−1 should be corrected for this limb effect variation. This correction increases this flow velocity to ∼70 m s−1. A search for a similar variation in plages and in network boundaries had negative results, the variation being +1%±5% and -1%±6% respectively.

Some comments on the limb shift of solar lines

Some comments on the limb shift of solar lines

Some comments on the limb shift of solar lines

Some comments on the limb shift of solar lines