Magnetospheric accretion and pre-main-sequence stellar masses

We present a method of determining lower limits on the masses of pre-main-sequence (PMS) stars and so constraining the PMS evolutionary tracks. This method uses the redshifted absorption feature observed in some emission-line profiles of T Tauri stars, indicative of infall. The maximum velocity of the accreting material measures the potential energy at the stellar surface, which, combined with an observational determination of the stellar radius, yields the stellar mass. This estimate is a lower limit owing to uncertainties in the geometry and projection effects. Using available data, we show that the computed lower limits can be larger than the masses derived from PMS evolutionary tracks for M   0.5 M. Our analysis also supports the notion that accretion streams do not impact near the stellar poles but probably hit the stellar surface at moderate latitudes.     

Strained co-ordinate methods in rotating stars

It was shown in a previous paper, Smith (1975), that the determination of the structure of rotating polytropes by expansion in the small rotational parameter constitutes asingular perturbation problem as arises also, for example, in large Reynolds' number approximations in fluid dynamics. The technique used by him — the method of matched asymptotic expansions — is, in fact, just an extension of the Prandtl boundary layer theory familiar in this latter context. In this paper — the first of two — we introduce an alternative procedure: the method of strained co-ordinates; and for comparison purposes again consider rotating polytropes. In Paper II we extend this approach to differentially rotating stars and present an illustrative example.     

An extension of Newton's apsidal precession theorem

Newton's apsidal precession theorem in Proposition 45 of Book I of the 'Principia' has great mathematical, physical, astronomical and historical interest. The lunar theory and the precession of the perihelion of the planet Mercury are but two examples of the applications of this theorem. We have examined the precession of orbits under varying force laws as measured by the apsidal angle θ( N , e ), where N is the index for the centripetal force law, for varying eccentricity e . The paper derives a general function for the apsidal angle, dependent only on e and N as the potential is spherically symmetric. Further, we explore approximate ways of the solution of this equation, in the neighbourhood of   N = 2  which happens to be the case of greatest historical interest. Exact solutions are derived where they are possible. The first derivatives  ∂θ/∂ N   and  ∂θ/∂ h   [where h ( N , e ) is the angular momentum] are analytically expressed in the neighbourhood of   N = 2  (case of the inverse square law). The value of  ∂θ/∂ N   is computed numerically as well for  1 ≤ N < 3  . The resulting integrals are interesting improper integrals with singularities at both limits. Some of the integrals, especially for   N = 2  , can be given in closed form in terms of generalized hypergeometric functions which are reducible in terms of algebraic and logarithmic functions. No evidence was found for isolated cases of zero precession as e was increased. The   N = 1  case of the logarithmic potential is also briefly discussed in view of its interest for the dynamics of eccentric orbits and its relevance to realistic galaxy models. The possibility of apsidal precession was also examined for a few cases of high-eccentricity asteroids and extrasolar planets. We find that these systems may provide interesting new laboratories for studies of gravity.     

A non-main-sequence secondary in SY Cancri

Simultaneous spectroscopic and photometric observations of the Z Cam type dwarf nova SY Cancri were used to obtain absolute flux calibrations. A comparison of the photometric calibration with a wide-slit spectrophotometric calibration showed that either method is equally satisfactory. A radial velocity study of the secondary star, made using the far-red Na  i doublet, yielded a semi-amplitude of   K ₂= 127 ± 23 km s⁻¹  . Taking the published value of  86 ± 9 km s⁻¹  for K ₁ gives a mass ratio of   q = M ₂/ M ₁= 0.68 ± 0.14  ; this is very different from the value of  1.13 ± 0.35  quoted in the literature. Using the new lower mass ratio, and constraining the mass of the white dwarf to be within reasonable limits, then leads to a mass for the secondary star that is substantially less than would be expected for its orbital period if it satisfied a main-sequence mass–radius relationship. We find a spectral type of M0 that is consistent with that expected for a main-sequence star of the low mass we have found. However, in order to fill its Roche lobe, the secondary must be significantly larger than a main-sequence star of that mass and spectral type. The secondary is definitely not a normal main-sequence star.     

New techniques of light curve analysis: Application to V444 Cygni

A new method of light curve analysis is introduced for systems containing one component possessing an extended atmosphere. Occultation or partial eclipses may be treated with or without the presence of transparency effects. Besides admitting an arbitrary degree of transparency to the eclipsing component, an arbitrary law of limb-darkening may also be assigned to the eclipsed star. The method is applied to the analysis of continuum, narrow band light curves of V444 Cygni obtained by Cherepashchuk and Khaliullin. Primary and secondary minima are examined separately with reasonable results.     

Far-infrared observations of main sequence stars surrounded by dust shells

We present 50 and 100µm photometry and size information for several main sequence stars surrounded by dust shells. The observations from NASA's Kuiper Airborne Observatory include the Vega-like stars, Beta Pic, Fomalhaut, as well as four stars suggested by Walker and Wolstencroft to belong possibly to the same class. The results of our observations are best interpreted as upper limits to the far-infrared sizes of the dust clouds around all of the stars except Fomalhaut and Beta Pic. We have also fit simple, optically thin models to the Beta Pic data to explore the range of shell parameters consistent with our limits and with previous observations.     

Pure pseudo-Cℓ estimators for CMB B-modes

Fast heuristically weighted, or pseudo-C_ℓ, estimators are a frequently used method for estimating power spectra in CMB surveys with large numbers of pixels. Recently, Challinor and Chon showed that the E–B mixing in these estimators can become a dominant contaminant at low noise levels, ultimately limiting the gravity wave signal which can be detected on a finite patch of sky. We define a modified version of the estimators which eliminates E–B mixing and is near-optimal at all noise levels.     

Effects of Faraday rotation observed in filter magnetograph data

In this paper we analyze the effects of Faraday rotation on the azimuth of a transverse magnetic field as determined from the linear polarization in the inverse Zeeman effect. Observations of a simple sunspot were obtained with the Marshall Space Flight Center's vector magnetograph over the wavelength interval of 170 mÅ redward of line center of the Fe i 5250.22 Å spectral line to 170 mÅ to the blue, in steps of 10 mÅ. These data were analyzed to produce the variation of the azimuth as a function of wavelength at each pixel over the field of view of the sunspot. At selected locations in the sunspot, curves of the observed variation of azimuth with wavelength were compared with model calculations for the azimuth at each wavelength as derived from the inverse Zeeman effect modified by Faraday rotation. From these comparisons we derived the maximum amount of rotation as functions of both the magnitude and inclination of the sunspot's field. These results show that Faraday rotation of the azimuth will be a significant problem in observations taken near the center of a spectral line for fields as low as 1200 G and inclinations of the field in the range 20–80 deg. Conversely, they show that measurements taken in the wing of a spectral line are relatively free of the effects of Faraday rotation.