Prolongation structure of the KdV equation in the bilinear form of Hirota

The prolongation structure of the KdV equation in the bilinear form of Hirota is determined, the resulting Lie algebra is realised and the Backlund transformation obtained from the prolongation structure is derived. The results are compared with those found by Wahlquist and Estabrook (1975) and by Hirota (1980)

An experimental study of counter-rotating cores in elliptical galaxies

Recent observational studies (Franx and Illingworth 1987; Jedrzejewski and Schechter 1988; Bender 1988; Illingworth and Franx 1989) have shown that some elliptical galaxies have a small region near the center that rotates in the opposite direction from the outer parts of the galaxy. Often the rotation in the central part is much faster than that in the outer part. A few other galaxies show a small region near the center that rotates in the same direction as the rest of the galaxy, but much faster. Either way, the part near the center that shows a strange pattern of rotation (the 'core') has been interpreted as a distinct dynamical subsystem. Very briefly, the observational data seem to be that anomalies show up in rotation curves near the centers of some elliptical galaxies and that galaxies with these strange rotational properties do not show a photometric signature: there are no noticeable bumps in the brightness profile and no unusual shapes of isophotal contours that would suggest an excess of matter concentrated near the center. No strong color variations have been reported. The puzzle is to learn what we can about elliptical galaxies in general, and about galaxies with strange central regions in particular, from these observational facts. The authors' approach is experimental. They make a guess about the form of the dynamically distinct subsystem, and then build a galaxy model to test experimental consequences such as the amount of matter required to produce observable effects and the length of time over which these effects would remain observable. They sidestep questions about how the galaxy might have gotten to be that way in the first place. That gives them more freedom to explore a variety of suggestions about what kind of dynamical system might give rise to the observed rotational patterns

The AM Canum Venaticorum binary SDSS J173047.59+554518.5

The AM Canum Venaticorum (AM CVn) binaries are a rare group of hydrogen-deficient, ultrashort period, mass-transferring white dwarf binaries and are possible progenitors of Type Ia supernovae. We present time-resolved spectroscopy of the recently discovered AM CVn binary SDSS J173047.59+554518.5. The average spectrum shows strong double-peaked helium emission lines, as well as a variety of metal lines, including neon; this is the second detection of neon in an AM CVn binary, after the much brighter system GP Com. We detect no calcium in the accretion disc, a puzzling feature that has been noted in many of the longer period AM CVn binaries. We measure an orbital period, from the radial velocities of the emission lines, of 35.2 ± 0.2 min, confirming the ultracompact binary nature of the system. The emission lines seen in SDSS J1730 are very narrow, although double-peaked, implying a low-inclination, face-on accretion disc; using the measured velocities of the line peaks, we estimate i ≤ 11°. This low inclination makes SDSS J1730 an excellent system for the identification of emission lines

Kinematics of the ultracompact helium accretor AM canum venaticorum

We report on the results from a five-night campaign of high-speed spectroscopy of the 17-min binary AM Canum Venaticorum (AM CVn), obtained with the 4.2-m William Herschel Telescope on La Palma. We detect a kinematic feature that appears to be entirely analogous to the 'central spike' known from the long-period, emission-line AM CVn stars GP Com, V396 Hya and SDSS J124058.03-015919.2, which has been attributed to the accreting white dwarf. Assuming that the feature indeed represents the projected velocity amplitude and phase of the accreting white dwarf, we derive a mass ratio q = 0.18 +/- 0.01 for AM CVn. This is significantly higher than the value found in previous, less direct measurements. We discuss the implications for AM CVn's evolutionary history and show that a helium star progenitor scenario is strongly favoured. We further discuss the implications for the interpretation of AM CVn's superhump behaviour, and for the detectability of its gravitational-wave signal with the Laser Interferometer Space Antenna (LISA). In addition, we demonstrate a method for measuring the circularity or eccentricity of AM CVn's accretion disc, using stroboscopic Doppler tomography. We test the predictions of an eccentric, precessing disc that are based on AM CVn's observed superhump behaviour. We limit the effective eccentricity in the outermost part of the disc, where the resonances that drive the eccentricity are thought to occur, to e = 0.04 +/- 0.01, which is smaller than previous models indicated

On the orbital periods of the AM CVn stars HP Librae and V803 Centauri

We analyse high-time-resolution spectroscopy of the AM CVn stars HP Librae and V803 Centauri, taken with the New Technology Telescope (NTT) and the Very Large Telescope (VLT) of the European Southern Observatory, Chile. We present evidence that the literature value for V803 Cen's orbital period is incorrect, based on an observed `S-wave' in the binary's spectrogram. We measure a spectroscopic period P=1596.4+/-1.2s of the S-wave feature, which is significantly shorter than the 1611-second periods found in previous photometric studies. We conclude that the latter period likely represents a `superhump'. If one assumes that our S-wave period is the orbital period, V803 Cen's mass ratio can be expected to be much less extreme than previously thought, at q~0.07 rather than q~0.016. This relaxes the constraints on the masses of the components considerably: the donor star does then not need to be fully degenerate, and the mass of the accreting white dwarf no longer has to be very close to the Chandrasekhar limit. For HP Lib, we similarly measure a spectroscopic period P=1102.8+/-0.2s. This supports the identification of HP Lib's photometric periods found in the literature, and the constraints upon the masses derived from them.Comment: Accepted for publication in MNRA

Phase-resolved spectroscopy of the helium dwarf nova 'SN 2003aw' in quiescence

High time resolution spectroscopic observations of the ultracompact helium dwarf nova 'SN 2003aw' in its quiescent state at V similar to 20.5 reveal its orbital period at 2027.8 +/- 0.5 s or 33.80 min. Together with the photometric 'superhump' period of 2041.5 +/- 0.5 s, this implies a mass ratio q approximate to 0.036. We compare both the average and time-resolved spectra of 'SN 2003aw' and Sloan Digital Sky Survey (SDSS) J124058.03-015919.2. Both show a DB white dwarf spectrum plus an optically thin, helium-dominated accretion disc. 'SN 2003aw' distinguishes itself from the SDSS source by its strong calcium H & K emission lines, suggesting higher abundances of heavy metals than the SDSS source. The silicon and iron emission lines observed in the SDSS source are about twice as strong in 'SN 2003aw'. The peculiar 'double bright spot' accretion disc feature seen in the SDSS source is also present in time-resolved spectra of 'SN 2003aw', albeit much weaker

TEMPERATURE MODIFICATION OF MALE SEX PHEROMONE RESPONSE AND FACTORS AFFECTING FEMALE CALLING IN HOLOMELINA IMMACULATA (LEPIDOPTERA: ARCTIIDAE)

In Holomelina immaculata (Reakirt) periodicity of male attraction to synthetic 2-methylheptadecane, the female-produced sex pheromone, is modified by temperature cues. In the field this response interval occurs from approximately sunset to about 4 h after sunset on a warm day and night (30° to 17 °C) and for the 2 h prior to sunset on a cool day and night (23° to 16 °C). In laboratory studies at 24 °C female H. immaculata placed in continual scotophase have an endogenous calling rhythm, but they are apparently inhibited from calling by constant photophase. In 16:8 or 12:12 light-dark cycles at 24 °C calling occurs from the 2nd to the 6th hour of scotophase, whereas at 15 °C calling takes place from the initiation to the 5th hour of scotophase. The critical cues governing initiation of calling behaviour are lights-off or a temperature decrease cue, and a temperature decrease signal overrides the apparent inhibitory effect of continual photophas