Studies of granular velocities

Vertical small scale velocities deduced from highly resolved spectra in the center of the solar disk, obtained with a RCA image intensifier tube, are discussed. As a main result we find that the velocities of small elements (< 2) are remarkably larger in active regions around sunspots than in the quiet Sun. In both cases the velocities decrease with height in the solar atmosphere (Figure 2).Mitteilungen aus dem Fraunhofer-Institut Nr. 145.     

Studies of granular velocities

The two available methods for determining the rms amplitude of the granular convective velocity field, namely the interpretation of line profiles, and direct measurements of velocity fluctuations in highly resolved spectra, give values ( 2 km/sec, and 0.4 km/sec, resp.) which are apparently inconsistent both in magnitude and in their dependence upon optical depth. We give both theoretical and observational evidence for the working hypothesis, that the best resolved spectra mainly show velocity fluctuations due to the oscillation of the solar atmosphere, whereas the contribution of the granular velocity field is greatly reduced because of atmospheric seeing and can be found only as a weak superposition to the oscillatory velocity field. Realistic assumptions for the typical size of the granulation (2.5) and for the seeing parameter (1), together with a simplified model of the granular velocity field, lead to correction factors of 30 to 40 between the true and observed amplitudes of the granular velocities.Mitteilungen aus dem Fraunhofer Institut, Nr. 95.     

Studies of granular velocities

Observations of quiescent solar prominences with the Harvard College Observatory spectrometer abroad Skylab show that prominence material is optically thick in the Lyman alpha line and the Lyman continuum. The color temperature of the Lyman continuum has a mean of 6600 K and an upward gradient toward the top of the prominence. The departure coefficient of the ground state of hydrogen is found to be of the order of unity as expected from theory. The optical depth of the Ciii sheath region is determined directly from the observation of the limb through the prominence and used to infer the mean electron density and the temperature gradient of the sheath. The result implies that the sheath density is about 0.4, and the temperature gradient about 1.4 times the respective value in the Ciii transition zone of the quiet Sun. The Ciii triplet-singlet ratio for the prominence is found to give a density compatible, within the uncertainty of the atomic parameters, with the density obtained from the optical depth. The Oviλ1032 line, which is emitted by both the prominence and the surrounding corona, is used to obtain an estimate of the thickness of the outer transition sheath of the prominence.     

Studies of granular velocities

Spectral observations of solar velocity fields made during a partial solar eclipse are described. Continuum intensity measurements at the lunar limb allow the modulation transfer function to be derived and the true spatial power spectrum of the velocity field to be reconstructed. The oscillatory and granular components are separated by applying spatial filters cutting off at 3.7. The oscillatory component values are in good agreement with those of Canfield (1976) but the granular component has substantially more power and a smaller height gradient. The discrepancy can be resolved by noting the uncertainties of the seeing corrections and of the separation into components in the work of Canfield.However on the basis of this limited material, we would go no further than to claim that the height dependence of the granular velocities remains an open question.Mitteilung aus dem Fraunhofer-Institut Nr. 157.     

Studies of granular velocities

Observations with the image intensifier tube at the Coudé refractor in Capri seem to confirm that the velocity field near sunspots contains more small scale fluctuations than in non-active regions, and that these fluctuations decrease more rapidly with height.Mitteilung aus dem Fraunhofer Institut Nr. 130.     

Studies of granular velocities

The process of measuring granular velocity fields with an instrument having finite spectral and spatial resolution is investigated for the case that (1) a weak Fraunhofer line is used, (2) the velocity is constant with height in the solar atmosphere, (3) the original Doppler shifts are of the same order of magnitude as the intrinsic width of the line (width observed with infinitely high spectral and spatial resolution), (4) continuum brightness and line strength fluctuations are superimposed onto the velocity field.It is shown that using a spectral instrumental profile which is large compared to both the intrinsic line width and the rms Doppler shifts (as in the case of filtergrammes), the shift-induced brightness signal is always a linear function of the shift and corrections for finite spatial resolution can be applied to the measured shifts in the usual straightforward way.If the spectral instrumental profile is not large (as in the case of slit-spectrogrammes), the observed line profile is shown to depend upon the spatial resolution as well. It is altered (broadened, made asymmetric) by (1) spatially unresolved Doppler shifts and higher moments of the Doppler shift amplitude distribution, (2) by local correlation between continuum brightness, line strength, and velocity fluctuation. A value of the Doppler shift which is unaffected by nonlinearities, can be measured at a certain position in the line wing. Knowledge of the intrinsic line width is necessary, however, to determine this position, as well as the order of magnitude of the nonlinearity effects producing asymmetries in the observed line profile. Finally, the conditions are discussed under which a complete deconvolution of a spectrum could be accomplished.On leave from Fraunhofer Institut, Freiburg.     

The height variation of granular and oscillatory velocities

Previous observations of spatially-resolved vertical velocity variations in ten lines of Fe i spanning the height range 0 h 1000 km are re-analyzed using velocity weighting functions. The amplitudes and scale heights of granular and oscillatory velocities are determined, as well as those of the remaining unresolved velocities. I find that the optimal representation of the amplitude of the outward-decreasing granular velocities is an exponentially decreasing function of height, with a scale height of 150 km and a velocity at zero height of 1.27 km s^–1. The optimal representation of the same quantities for oscillatory velocities is an exponential increase with height, with a scale height of 1100 km and a velocity at zero height of 0.35 km s^–1. The remaining unresolved velocities decrease with height, with a scale height of 380 km and a velocity at zero height of 2.3 km s^–1.     

A power spectrum analysis of granular intensity fluctuations and velocities

An exceptionally highly resolved spectrogram (obtained by W. Livingston at Kitt Peak) has been used to derive rms values for both the intensity fluctuations in the continuum and the granular velocities in the Baii line 5853.69 by means of the power spectrum analysis. The main results are: (1) a corrected rms value for the intensity fluctuations of 3.8%; (2) a nearly constant power level in the one-dimensional power spectrum per unit wave number within the range 0.00018–0.01 km^-1 (34000 km-600km); (3) a corrected rms value for the granular velocities of 1 km/s.The behaviour of the asymmetry of the Ban line in individual bright and dark continuous streaks can be explained by a superposition of two shifted symmetric line profiles originating from pure granular and intergranular regions, respectively. The impurity of dark and bright streaks amounts to be less than 10%, the mean relative velocity of granular and intergranular regions being again 1 km/s. We find indications the microturbulence in the intergranular regions to be larger than in the granular ones.     

Pulsar velocities

Radio pulsars have long been established as having high velocities that are probably produced in the violence of their formation in Supernovae (Gunn & Ostriker 1970; Lyne, Anderson & Salter 1982). Three recent developments have resulted in a reassessment of their velocities: the adoption of a new distance scale (Taylor & Cordes 1993), many new determinations of proper motion (Harrison, Lyne & Anderson 1993; Bailes et al. 1989; Fomalont et al. 1992) and the realisation (Harrison & Lyne 1993) that estimates of speeds derived from scintillation measurements were systematically low by about a factor of 2. Taking into account a strong selection effect that makes the observed velocities unrepresentative of those acquired at birth, it seems that the mean space velocity of pulsars at birth is 450 ± 90 km s^-1 (Lyne and Lorimer 1994), about a factor of 3 greater than earlier estimates. The general migration from the Galactic plane is consistent with birth in the supernova of massive Population I stars. An outstanding question is how such velocities are produced in the kinetics of supernova collapse. This large increase in birth velocity is likely to have a major impact upon our understanding of the retention of neutron stars in binary systems, globular clusters and the Galaxy as it exceeds or is comparable with all their escape velocities. The rapid spatial separation of fast and slow pulsars will have a profound effect upon calculations of the galactic population and birth rate, both of which have been underestimated in the past. Furthermore, the distribution of dead neutron stars will be more isotropic and may better match the distribution of the gamma-ray burst sources. A small number of pulsars are at a large distance from the Galactic plane, but moving towards it. The most likely origin of these objects lies in OB runaway stars.     

Millisecond pulsar velocities

We present improved timing parameters for 13 millisecond pulsars (MSPs), including nine new proper motion measurements. These new proper motions bring to 23 the number of MSPs with measured transverse velocities. In light of these new results we present and compare the kinematic properties of MSPs with those of ordinary pulsars. The mean transverse velocity of MSPs was found to be 85±13 km s⁻¹, a value consistent with most models for the origin and evolution of MSPs and approximately a factor of 4 lower than that of ordinary pulsars. We also find that, in contrast to young ordinary pulsars, the vast majority of which are moving away from the Galactic plane, almost half of the MSPs are moving towards the plane. This near-isotropy would be expected of a population that has reached dynamic equilibrium. Accurate measurements of MSP velocities have allowed us to correct their measured spin-down rates for Doppler acceleration effects, and thereby derive their intrinsic magnetic field strengths and characteristic ages. We find that close to half of our sample of MSPs have a characteristic age comparable to or greater than the age of the Galactic disc.     

Spatial velocities of pulsars

Assuming that the orientation of a pulsar’s velocity vector is parallel to its spin axis, we have calculated the space velocities of 61 pulsars from their tangential velocities. The mean space velocity of the sample is equal to 267 km s^-1. The radial velocities and kinematical ages of 20 pulsars are obtained. The decay time of the magnetic field of pulsars is τ_D = 2 Myr, smaller than previously found     

Tide-induced perturbations of glacier velocities

Recent observations showing substantial diurnal changes in velocities of glaciers flowing into the ocean, measured at locations far inland of glacier grounding lines, add fuel to the ongoing debate concerning the ability of glaciers to transmit longitudinal-stress perturbations over large distances. Resolution of this debate has major implications for the prediction of glacier mass balance, because it determines how rapidly a glacier can respond dynamically to changes such as weakening or removal of an ice shelf. Current IPCC assessment of sea-level rise takes little account of such changes, on the assumption that dynamic responses would be too slow to have any appreciable effect on ice discharge fluxes. However, this assumption must be questioned in view of observations showing massive increases in glacier velocities following removal of parts of the Larsen Ice Shelf, Antarctica, and of others showing diurnal velocity changes apparently linked to the tides.Here, I use a simple force-perturbation model to calculate the response of glacier strain rates to tidal rise and fall, assuming associated longitudinal-force perturbations are transmitted swiftly far inland of the glacier grounding line. Results show reasonable agreement with observations from an Alaskan glacier, where the velocity changes extended only a short distance up-glacier. However, for larger Antarctic glaciers, big velocity changes extending far upstream cannot be explained by this mechanism, unless ice-shelf “back forces” change substantially with the tides.Additional insight will require continuous measurement of velocity and strain-rate profiles along flow lines of glaciers and ice shelves. An example is suggested, involving continuous GPS measurements at a series of locations along the centre line of Glaciar San Rafael, Chile, extending from near the calving front to perhaps 20 km inland. Tidal range here is about ± 0.8 m, which should be sufficient to cause a variation in ice-front velocity of ± 2 cm h^− 1 about its average value of 75 cm h^− 1, assuming local seawater depth of 150 m and glacier thickness of 200–400 m.     

Expansion velocities of cometary gas

Heating processes are expected to strongly affect the structure and dynamics of cometary comas. A radial expansion velocity of less than 1 km s^–1 in the inner coma is quite compatible with a few km s^–1 in the outer regions of large comets.     

Infrared velocities of carbon stars

We present CS(J = 1 0) observations of the high density gas in a sample of eleven star forming regions with molecular or optical outflows. The sources of this sample cover a wide range of physical sizes. All these sources had been previously mapped in NH₃ (1,1) with similar angular resolution. In all the sources of this sample CS emission was detected, indicating a global correlation between the emissions traced by the CS and the NH₃ molecules. However, the detailed characteristics of these two emissions (e.g., the extent and the location of the emission peak) show, in general, significant differences in the sources which are well resolved by the beam. As a general trend, the emission traced by the NH₃ molecule appears as compact clumps which engulf an outflow activity center. In contrast, the emission traced by the CS molecule, usually more extended, appears as a background which connects different outflow activity centers associated with each NH₃ clump.     

Measurements of line-of-sight velocities in prominences

Measurements of line-of-sight velocities of quiescent and sunspot prominences on the limb made during the years 1966 and 1968 at Swedish Astrophysical Station in Anacapri, Italy are discussed. Several statistical properties of the velocity field, in particular its connection with close McMath plages are investigated. Results are interpreted in terms of oscillatory motion in prominences.     

Peculiar velocities of galaxies and clusters

We present a simple model for the shape of the distribution function of galaxy peculiar velocities. We show how both non-linear and linear theory terms combine to produce a distribution which has an approximately Gaussian core with exponential wings. The model is easily extended to study how the statistic depends on the type of particle used to trace the velocity field (dark matter particles, dark matter haloes, galaxies), and on the density of the environment in which the test particles are located. Comparisons with simulations suggest that our model is accurate. We also show that the evolution of the peculiar velocities depends on the local, rather than the global, density. Since clusters populate denser regions on average, using cluster velocities with the linear theory scaling may lead to an overestimate of the global value of Ω₀. Conversely, using linear theory with the global value of Ω₀ to scale cluster velocities from the initial to the present time results in an underestimate of their true velocities. In general, however, the directions of motions of haloes are rather well described by linear theory. Our results help to simplify models of redshift-space distortions considerably.     

Equilibrium velocities of a planetesimal population

The random velocities v(m) of planetesimal populations specified by maximum and minimum masses and a number density n(m) ∝ m^?q are calculated interatively based on two different physical models involving ratios of rates: (1) excitation of kinetic energy by gravitational perturbation and elastic collision equal to damping of kinetic energy by inelastic collisions; and (2) excitation of kinetic energy a ratio b (～3 usually) to doubling of mass. Model (2) follows the theory of Safronov closely. Both physical models are developed approximately, using averaged factors for collision dissipation and velocity ratios, and then more precisely, allowing for reference orbit differences and for plausible variations in collisional energy dissipation with impact velocity and planetesimal mass ratios. The approximate model (2) agrees reasonably well with the results of Safronov. Both precise models are applied to populations approximating those generated by the calculations of Greenberg, Cox, and Wetherill, producing qualitatively similar velocities v(m). These results encourage analytic models of planetesimal population growth, incrementing masses and calculating velocity distributions in alternate steps. The principal improvement needed in the models is more realistic collision energy partitioning.