Comment on “Mathematical and physical aspects of Kappa velocity distribution” [ Phys. Plasmas 14, 110702 (2007) ]

A recent paper [L.-N. Hau and W.-Z. Fu, Phys. Plasmas 14, 110702 (2007)] deals with certain mathematical and physical properties of the kappa distribution. We comment on the authors' use of a form of distribution function that is different from the "standard" form of the kappa distribution, and hence their results, inter alia for an expansion of the distribution function and for the associated number density in an electrostatic potential, do not fully reflect the dependence on kappa that would be associated with the conventional kappa distribution. We note that their definition of the kappa distribution function is also different from a modified distribution based on the notion of nonextensive entropy.

A review of the equations used to predict the velocity distribution within a ship’s propeller jet

Predicting the velocity within the ship’s propeller jet is the initial step to investigate the scouring made by the propeller jet. Albertson et al. (1950) suggested the investigation of a submerged jet can be undertaken through observation of the plain water jet from an orifice. The plain water jet investigation of Albertson et al. (1950) was based on the axial momentum theory. This has been the basis of all subsequent work with propeller jets. In reality, the velocity characteristic of a ship’s propeller jet is more complicated than a plain water jet. Fuehrer and Römisch (1977), Blaauw and van de Kaa (1978), Berger et al. (1981), Verhey (1983) and Hamill (1987) have carried out investigations using physical model. This paper reviews the state-of-art of the equations used to predict the time-averaged axial, tangential and radial components of velocity within the zone of flow establishment and the zone of established flow of a ship’s propeller jet.

High-velocity features: A ubiquitous property of Type Ia supernovae

Evidence of high-velocity features (HVFs) such as those seen in the near-maximum spectra of some Type Ia supernovae (SNe Ia; e. g., SN 2000cx) has been searched for in the available SN Ia spectra observed earlier than 1 week before B maximum. Recent observational efforts have doubled the number of SNe Ia with very early spectra. Remarkably, all SNe Ia with early data ( seven in our Research Training Network sample and 10 from other programs) show signs of such features, to a greater or lesser degree, in Ca II IR and some also in the Si II lambda 6355 line. HVFs may be interpreted as abundance or density enhancements. Abundance enhancements would imply an outer region dominated by Si and Ca. Density enhancements may result from the sweeping up of circumstellar material (CSM) by the highest velocity SN ejecta. In this scenario, the high incidence of HVFs suggests that a thick disk and/or a high-density companion wind surrounds the exploding white dwarf, as may be the case in single degenerate systems. Large-scale angular fluctuations in the radial density and abundance distribution may also be responsible: this could originate in the explosion and would suggest a deflagration as the more likely explosion mechanism. CSM interaction and surface fluctuations may coexist, possibly leaving different signatures on the spectrum. In some SNe, the HVFs are narrowly confined in velocity, suggesting the ejection of blobs of burned material.

Exoplanets or Dynamic Atmospheres? The Radial Velocity and Line Shape Variations of 51 Pegasi and tau Bootis

The stars 51 Pegasi and tau Bootis show radial velocity variations that have been interpreted as resulting from companions with roughly Jovian mass and orbital periods of a few days. Gray and Gray & Hatzes reported that the radial velocity signal of 51 Peg is synchronous with variations in the shape of the line lambda 6253 Fe I; thus, they argue that the velocity signal arises not from a companion of planetary mass but from dynamic processes in the atmosphere of the star, possibly nonradial pulsations. Here we seek confirming evidence for line shape or strength variations in both 51 Peg and tau Boo, using R = 50,000 observations taken with the Advanced Fiber Optic Echelle. Because of our relatively low spectral resolution, we compare our observations with Gray's line bisector data by fitting observed line profiles to an expansion in terms of orthogonal (Hermite) functions. To obtain an accurate comparison, we model the emergent line profiles from rotating and pulsating stars, taking the instrumental point-spread function into account. We describe this modeling process in detail. We find no evidence for line profile or strength variations at the radial velocity period in either 51 Peg or in tau Boo. For 51 Peg, our upper limit for line shape variations with 4.23 day periodicity is small enough to exclude with 10 sigma confidence the bisector curvature signal reported by Gray & Hatzes; the bisector span and relative line depth signals reported by Gray are also not seen, but in this case with marginal (2 sigma ) confidence. We cannot, however, exclude pulsations as the source of 51 Peg's radial velocity variation because our models imply that line shape variations associated with pulsations should be much smaller than those computed by Gray & Hatzes; these smaller signals are below the detection limits both for Gray & Hatzes's data and for our own. tau Boo's large radial velocity amplitude and v sin i make it easier to test for pulsations in this star. Again we find no evidence for periodic line shape changes, at a level that rules out pulsations as the source of the radial velocity variability. We conclude that the planet hypothesis remains the most likely explanation for the existing data.

Stellar jitter from variable gravitational redshift: implications for radial velocity confirmation of habitable exoplanets

A variation of gravitational redshift, arising from stellar radius fluctuations, will introduce astrophysical noise into radial velocity measurements by shifting the centroid of the observed spectral lines. Shifting the centroid does not necessarily introduce line asymmetries. This is fundamentally different from other types of stellar jitter so far identified, which do result from line asymmetries. Furthermore, only a very small change in stellar radius, ˜0.01 per cent, is necessary to generate a gravitational redshift variation large enough to mask or mimic an Earth-twin. We explore possible mechanisms for stellar radius fluctuations in low-mass stars. Convective inhibition due to varying magnetic field strengths and the Wilson depression of starspots are both found to induce substantial gravitational redshift variations. Finally, we investigate a possible method for monitoring/correcting this newly identified potential source of jitter and comment on its impact for future exoplanet searches.

The velocity distribution of solar photospheric magnetic bright points.

We use high spatial resolution observations and numerical simulations to study the velocity distribution of solar photospheric magnetic bright points. The observations were obtained with the Rapid Oscillations in the Solar Atmosphere instrument at the Dunn Solar Telescope, while the numerical simulations were undertaken with the MURaM code for average magnetic fields of 200 G and 400 G. We implemented an automated bright point detection and tracking algorithm on the data set and studied the subsequent velocity characteristics of over 6000 structures, finding an average velocity of approximately 1 km s(-1), with maximum values of 7 km s(-1). Furthermore, merging magnetic bright points were found to have considerably higher velocities, and significantly longer lifetimes, than isolated structures. By implementing a new and novel technique, we were able to estimate the background magnetic flux of our observational data, which is consistent with a field strength of 400 G.

Distance limits to intermediate- and high-velocity clouds

We present optical spectra of 403 stars and quasi-stellar objects in order to obtain distance limits towards intermediate- and high-velocity clouds (IHVCs), including new Fibre-fed Extended Range Optical Spectrograph (FEROS) observations plus archival ELODIE, FEROS, High Resolution Echelle Spectrometer (HIRES) and Ultraviolet and Visual Echelle Spectrograph (UVES) data. The non-detection of Ca II K interstellar (IS) absorption at a velocity of −130 to −60 km s−1 towards HDE 248894 (d ∼ 3 kpc) and HDE 256725 (d ∼ 8 kpc) in data at signal-to-noise ratio (S/N) > 450 provides a new firm lower distance limit of 8 kpc for the anti-centre shell HVC. Similarly, the non-detection of Ca II K IS absorption towards HD 86248 at S/N ∼ 500 places a lower distance limit of 7.6 kpc for Complex EP, unsurprising since this feature is probably related to the Magellanic System. The lack of detection of Na I D at S/N = 35 towards Mrk 595 puts an improved upper limit for the Na I column density of log (NNaD <) 10.95 cm−2 towards this part of the Cohen Stream where Ca II was detected by Wakker et al. Absorption at ∼ −40 km s−1 is detected in Na I D towards the Galactic star PG 0039+049 at S/N = 75, placing a firm upper distance limit of 1 kpc for the intermediate-velocity cloud south (IVS), where a tentative detection had previously been obtained by Centurion et al. Ca ´ II K and Na I D absorption is detected at −53 km s−1 towards HD 93521, which confirms the upper distance limit of 2.4 kpc for part of the IV arch complex obtained using the International Ultraviolet Explorer (IUE) data by Danly. Towards HD 216411 in Complex H a non-detection in Na D towards gas with log(NH I) = 20.69 cm−2 puts a lower distance limit of 6.6 kpc towards this HVC complex. Additionally, Na I D absorption is detected at −43.7 km s−1 in the star HD 218915 at a distance of 5.0 kpc in gas in the same region of the sky as Complex H. Finally, the Na I/Ca II and Ca II/H I ratios of the current sample are found to lie in the range observed for previous studies of IHVCs.

Study of ground-state titanium ion velocity distributions in laser-produced plasma plumes

The velocity distribution of ground-state titanium ions within a low-temperature plasma resulting from the laser ablation of a titanium target has been investigated. A KrF excimer laser was focused onto the target at moderate fluences (