A method of measuring the solar rotation

We propose a method to determine the surface velocity of solar rotation. The method rests on measurement of the line-of-sight velocity difference between two elements on the solar disk which are symmetric about the central meridian at the same heliolatitude. This is a simple method which is largely free from the influence of spectrograph noise and instrumental drifts and permits several measurements to be made during one day. Results of trial observations are reported. The rotation curve we have obtained is notable for the large value of equatorial velocity as well as a steeper dip with increasing latitude.     

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.     

Orbital structure of the GJ876 extrasolar planetary system based on the latest Keck and HARPS radial velocity data

We use full available array of radial velocity data, including recently published HARPS and Keck observatory sets, to characterize the orbital configuration of the planetary system orbiting GJ876. First, we propose and describe in detail a fast method to fit perturbed orbital configuration, based on the integration of the sensitivity equations inferred by the equations of the original N-body problem. Further, we find that it is unsatisfactory to treat the available radial velocity data for GJ876 in the traditional white noise model, because the actual noise appears autocorrelated (and demonstrates non-white frequency spectrum). The time scale of this correlation is about a few days, and the contribution of the correlated noise is about 2 m/s (i.e., similar to the level of internal errors in the Keck data). We propose a variation of the maximum-likelihood algorithm to estimate the orbital configuration of the system, taking into account the red noise effects. We show, in particular, that the non-zero orbital eccentricity of the innermost planet d, obtained in previous studies, is likely a result of misinterpreted red noise in the data. In addition to offsets in some orbital parameters, the red noise also makes the fit uncertainties systematically underestimated (while they are treated in the traditional white noise model). Also, we show that the orbital eccentricity of the outermost planet is actually ill-determined, although bounded by ~0.2. Finally, we investigate possible orbital non-coplanarity of the system, and limit the mutual inclination between the planets b and c orbits by 5°?C15°, depending on the angular position of the mutual orbital nodes.     

Development of an Absolute Accelerometer for Extra-Solar Planet Detection

The method of stellar radial velocity variations has recently shown its capability by the first discovery of several extra-solar planets. Accuracies achieved today are in the range 3-10 m/s. The AAA (absolute astronomical accelerometer) is an instrument which aims to reach the photon noise limit for the measurement of velocity changes, with systematic errors of about 1 m/s, long term. The principle is to use a servo-controlled CCD spectrograph as a null detector, and to register always the lines of the star on the same CCD pixels. Thus, systematic errors linked to the Earth-induced large variations are cancelled. A tunable Fabry-Perot channelled spectrum is also following the star spectrum, while the FP thickness is measured by heterodyne detection of the beats between a tunable laser diode and a stabilized laser diode. A complete prototype of the instrument is operating with laboratory sources and the first results are presented. It is planned to use this system with a new spectrograph, to be coupled to the 152 cm telescope at Observatoire de Haute Provence.     

Steady heat conduction in coronal loop unstable against plasma instability

The Fokker-Planck equation is numerically solved to study the electron velocity distribution under steady heat conduction with an applied axial electric current in a model coronal loop.If the loop temperature is so high that the electron mean-free path is longer than the local temperature scale height along the loop, a velocity hump appears at about the local thermal electron velocity. The hump is attributed to cooler electrons moving up the temperature gradient to compensate for the runaway electrons moving down the gradient. If the ratio between the mean free path and temperature scale height is greater than about 2, negative absorption for the plasma waves can appear (waves grow). This effect is enhanced by the presence of axial electric current in the half of the coronal loop in which the electrons carrying the current are drifting up the temperature gradient. Thus, the plasma instability may occur in the coronal elementary magnetic flux tubes. Although the present paper is limited to show the critical condition and linear growth rate of the instability, the following scenarios may be inferred.If the flux tubes change from marginally stable to unstable against the plasma instability, due to an increase in the loop temperature, anomalous resistivity may suddenly appear because of the growth of plasma waves. Then a high axial electric field is induced that may accelerate particles. This could be the onset of impulsive loop flares.For a low electric current, if the loop temperature is sufficiently high to give the negative absorption for the plasma waves in a large part of the coronal loop, steady plasma turbulence may originate. This could be a source for the type I radio noise storm.     

Automatic Recognition and Characterisation of Supergranular Cells from Photospheric Velocity Fields

We have developed an exceptionally noise-resistant method for accurate and automatic identification of supergranular cell boundaries from velocity measurements. Because of its high noise tolerance the algorithm can produce reliable cell patterns with only very small amounts of smoothing of the source data in comparison to conventional methods. In this paper we describe the method and test it with simulated data. We then apply it to the analysis of velocity fields derived from high-resolution continuum data from MDI (Michelson Doppler Imager) on SOHO. From this, we can identify with high spatial resolution certain basic properties of supergranulation cells, such as their characteristic sizes, the flow speeds within cells, and their dependence on cell areas. The effect of the noise and smoothing on the derived cell boundaries is investigated and quantified by using simulated data. We show in detail the evolution of supergranular cells over their lifetime, including observations of emerging, splitting, and coalescing cells. A key result of our analysis of cell internal velocities is that there is a simple linear relation between cell size and cell internal velocity, rather than the power law usually suggested. Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.     

On the potential of transit surveys in star clusters: impact of correlated noise and radial velocity follow-up

We present an extension of the formalism recently proposed by Pepper and Gaudi to evaluate the yield of transit surveys in homogeneous stellar systems, incorporating the impact of correlated noise on transit time-scales on the detectability of transits, and simultaneously incorporating the magnitude limits imposed by the need for radial velocity (RV) follow-up of transit candidates. New expressions are derived for the different contributions to the noise budget on transit time-scales and the least-squares detection statistic for box-shaped transits, and their behaviour as a function of stellar mass is re-examined. Correlated noise that is constant with apparent stellar magnitude implies a steep decrease in detection probability at the high -mass end which, when considered jointly with the RV requirements, can severely limit the potential of otherwise promising surveys in star clusters. However, we find that small-aperture, wide-field surveys may detect hot Neptunes whose RV signal can be measured with present-day instrumentation in very nearby (<100 pc) clusters.     

Gravity gradient mapping from the lunar polar orbiter - a simulation study

Simulations of the gravity data to be expected from a Lunar Polar Orbiter spacecraft utilizing either a Doppler velocity tracking system or a gravity gradiometer instrument system are generated using a point mass model that gives an excellent representation of the types of gravity anomalies to be found on the Moon. If the state of the art in instrumentation of both systems remain at the level of ±1 mm/sec at 10 sec integration time for the Doppler velocity system accuracy and at ±1 Eotvos at 10 sec integration time for the gravity gradiometer system accuracy, inspection of the simulations indicates that a gravity gradiometer system will give science data with better resolution and higher amplitude-to-measurement noise ratio than the Doppler velocity system at altitudes below 100 km. The error model used in the study is one where the system errors are assumed to be dominated by the point measurement noise and data quantization noise. The effects of other, more controllable, systematic error sources are not considered in this simplified analysis. For example, both systems will be affected by errors in LPO orbital altitude and position knowledge, spacecraft maneuvers, and data reduction errors. In addition, a Doppler tracking system will be sensitive to errors produced by spacecraft acceleration (from outgassing or solar pressure) and poor relative position of the LPO, Relay Satellite and ground tracking station, while a gravity gradiometer system will be sensitive to errors from spacecraft attitude and angular rates. These preliminary study results now need to be verified by a more complete error analysis in which all the uncertainties of the data gathering process are formally mapped into uncertainties in the resulting gravity maps.     

On the determination of noise in photographic measurements of solar velocities and magnetic fields

The noise in photographic measurements of solar velocities and magnetic fields is assumed to be essentially determined by the granularity of the film, its gamma, the scanning spot size and the parameters of the specific spectral line. A formula is derived which serves for a quantitative estimate of the rms velocity and magnetic field noise when evaluating spectrograms and spectroheliograms. Four typical examples are treated and show that the estimate is correct within 20%.Mitteilungen aus dem Fraunhofer Institut Nr. 118.     

Electro-hydromagnetic waves in a fully ionized gas—I

Transport equations are used to determine coefficients which are generalizations for any frequency of electric field of the parallel, Pedersen and Hall conductivities in a fully ionized gas.

These coefficients are used in an investigation of the propagation of weak electromagnetic and hydromagnetic waves of all frequencies across a homogeneous and constant magnetic field in a rarefied fully ionized gas. For propagation perpendicular to the magnetic field it is found for all frequencies

(i)

(ii)

where V² = H²/4π and v, h are the perturbations of the velocity, magnetic field. Similar relationships are deduced for propagation at any angle to the field for frequencies greater than about 10 times the gyrofrequency of electrons.

The theory is applied to discuss transmission of disturbance across the interplanetary medium, the temperature of the solar corona and the earth's outer atmosphere, the emission of non-thermal solar radio noise, cosmic radio noise and the anomalous emission of light from shock fronts.     

General presentation of a single IRIS site raw data analysis problem

A complete software package has been built for the calibration in m s ^–1 of the velocity residuals due to solar oscillations in the raw IRIS (International Research on the Interior of the Sun) data. It takes into account all known astronomical components contributing to the line-of-sight velocity between the instrument and the solar surface, and also the apparent velocity due to the non-uniform integration of the solar rotation as seen through an inhomogeneous Earth atmosphere. The IRIS data itself is used for the estimation of the nonlinear instrumental response to the velocity, and the residual can be directly obtained in velocity units, without low frequency filtering. On a day of typical photometric sky quality, the power spectrum obtained appears to be solar noise limited.     

Le guidage des whistlers par le champ magnetique

In this paper the question is examined of how the v.l.f. radio-waves are guided along the magnetic field. Energy passes through the magnetic field under two sets of conditions. Corresponding to the “nose-whistlers” explained by Helliwell, the first one occurs when the wave-normal itself is in the direction of the magnetic field. This does not happen in the second case when the remarkable property is also shown that all frequencies are propagated at the same velocity V₀ = cƒ_H/2ƒ₀ (ƒ_H gyrofrequency, ƒ₀ frequency of the plasma). Considerations of energy point out that, if such a propagation is not easily observable in the case of an isotropic emission, it is not the same thing for an emission produced by erenkov effect, which is able to produce all energy by this mode of propagation, provided the particle's velocity has a low fixed value (˜ 10,000 km/sec in the exosphere). All frequencies being emitted at the same time and following the same path wtih the same velocity, we can explain the broadband noise observed during the reception of whistlers. The required velocity of particles is exactly the velocity V₀. This coincidence is explained in an appendix, and extended to other anisotropic media.     

Test of a differential photometer for extinction gradient correction in full-disk helioseismology

The ground based full disk velocity Doppler measurements used in helioseismology suffer from an atmospheric noise component when the sky transparency is not perfect. It is due to the non uniform integration of the line of sight component of the solar rotation produced by the differential atmospheric extinction across the direction of the solar equator. A simple two-channel differential photometer is proposed for measuring this differential extinction. The first laboratory tests of this instrument show that it has the capability of performing the required correction without adding a significant level of new instrumental noise contribution.

     

Relation of Velocity Distribution and Mass for DA White Dwarfstwo

White dwarfs are the evolutionary endpoint of the low-and-medium mass stars. In the studies of white dwarfs, the mass of white dwarf is an important physical parameter. In this paper, we give an analysis about the velocity distribution of DA white dwarfs in the Sloan Digital Sky Survey (SDSS), and hope to find the relation between mass and velocity distribution of white dwarfs. We get the radial velocity and tangential velocity of every DA white dwarf according to their proper motion and spectral shift. Through analyzing the velocity distribution of DA white dwarfs, we find that the small-mass white dwarfs, which are produced from the single-star evolution channel, have a relatively large velocity dispersion.     

估计Be星自转的一个统计方法

本文给出了一个统计方法,可以由观测得到的Be星视自转速度U=V sin i,估计出其真自转速度V;本文证实了Be星不是以临界速度旋转的,其真自转速度和临界速度之比为0.7左右。     

Todcor: A TwO-Dimensional CORrelation technique to analyze stellar spectra in search of faint companions

TODCOR is a new TwO-Dimensional CORrelation technique to measure radial velocities of two components of a spectroscopic binary. Assuming the spectra of the two components are known, the technique correlates an observed binary spectrum against a combination of the two spectra with different shifts. TODCOR measuressimultaneously the radial velocities of the two stars by finding the maximum correlation.One of the advantages of TODCOR is its ability to detect a very faint companion in a combined spectrum, and to measure its radial velocity. We performed numerous tests in which we applied TODCOR to simulated spectra which were prepared as combinations of two spectra with various luminosity ratios, together with random noise. These tests show that TODCOR can detect a very faint secondary spectrum and measure correctly its velocity, even with a luminosity ratio of 1000, provided the combined spectrum has enough spectral coverage and highS / N. Measuring the radial velocity of the faint secondary will enable us to estimate the companion mass, a very useful tool in the search for brown dwarfs and giant planets around nearby stars.Paper presented at the Conference onPlanetary Systems: Formation, Evolution, and Detection held 7–10 December, 1992 at CalTech, Pasadena, California, U.S.A.     

Precision timing measurements of PSR J1012+5307

We present results and applications of high-precision timing measurements of the binary millisecond pulsar J1012+5307. Combining our radio timing measurements with results based on optical observations, we derive complete 3D velocity information for this system. Correcting for Doppler effects, we derive the intrinsic spin parameters of this pulsar and a characteristic age of 8.6±1.9 Gyr . Our upper limit for the orbital eccentricity of only 8×10⁻⁷ (68 per cent confidence level) is the smallest ever measured for a binary system. We demonstrate that this makes the pulsar an ideal laboratory in which to test certain aspects of alternative theories of gravitation. Our precision measurements suggest deviations from a simple pulsar spin-down timing model, which are consistent with timing noise and the extrapolation of the known behaviour of slowly rotating pulsars.     

Lunar orbit determination in the presence of unmodeled accelerations

A technique for estimating the state of an artificial satellite in the presence of unmodeled accelerations is presented. The unmodeled acceleration is approximated by a first-order Gauss-Markov sequence which can be separated into a timewise correlated component and a purely random component. Using this approximation, a sequential procedure for estimating the position, velocity, and the unmodeled acceleration is developed. The method is evaluated by reducing range-rate observations obtained by tracking the Apollo 10 and 11 spacecraft during the lunar orbit phase of the mission. Numerical results are presented which show that the observation residual pattern lies within the observation noise standard deviation. The values of the estimated components of the unmodeled acceleration are repeatable from orbit to orbit within a given mission and from mission to mission when the same ground track is covered. Finally, the variation in the radial component of the unmodeled acceleration shows a high correlation with the reported location of the lunar surface mascons.     

An explanation for lapetus' asymmetric reflectance

Cook and Franklin (1970, Icarus 13, 282) consider Iapetus originally to have been coated with about a meter of ice. They suggest that Iapetus' orbital velocity about Saturn has caused an asymmetric erosion of this ice layer which has now nearly laid bare its “leading” hemisphere, but not as yet the entire “trailing” hemisphere. Rather than an erosion process which operates more actively on the leading side, this paper considers an ice deposition mechanism operating more actively on the trailing side. The two main assumptions used are (1) that there are more icy than rocky meteoroids in Saturn's environment, and (2) that some portion of each icy meteoroid will stick to a surface at collision velocities less than 2.4kmsec^?1, but will completely vaporize itself at greater velocities. A meteoroid can have the minimum collision velocity of about 1.7kmsec^?1 with Iapetus only if their velocity vectors are nearly parallel, and under these conditions such collisions would tend to be with the trailing hemisphere. Collisions with the leading hemisphere will tend to be at a much higher velocity.