Graphs of relations and Hilbert series

We are discussing certain combinatorial and counting problems related to quadratic algebras. First we give examples which confirm the Anick conjecture on the minimal Hilbert series for algebras given by $n$ generators and $\frac {n(n-1)}{2}$ relations for $n \leq 7$. Then we investigate combinatorial structure of colored graph associated to relations of RIT algebra. Precise descriptions of graphs (maps) corresponding to algebras with maximal Hilbert series are given in certain cases. As a consequence it turns out, for example, that RIT algebra may have a maximal Hilbert series only if components of the graph associated to each color are pairwise 2-isomorphic.

Serendipitous Asteroid Lightcurve Survey Using SuperWASP

The SuperWASP project is an ultra-wide angle search for extra solar planetary transits. However, it can also serendipitously detect solar system objects, such as asteroids and comets. Each SuperWASP instrument consists of up to eight cameras, combined with high-quality peltier-cooled CCDs, which photometrically survey large numbers of stars in the magnitude range 7 15. Each camera covers a 7.8 × 7.8 degree field of view. Located on La Palma, the SuperWASP-I instrument has been observing the Northern Hemisphere with five cameras since its inauguration in April 2004. The ultra-wide angle field of view gives SuperWASP the possibility of discovering new fast moving (near to Earth) asteroids that could have been missed by other instruments. However, it provides an excellent opportunity to produce a magnitude-limited lightcurve survey of known main belt asteroids. As slow moving asteroids stay within a single SuperWASP field for several weeks, and may be seen in many fields, a survey of all objects brighter than magnitude 15 is possible. This will provide a significant increase in the total number of lightcurves available for statistical studies without the inherent bias against longer periods present in the current data sets. We present the methodology used in the automated collection of asteroid data from SuperWASP and some of the first examples of lightcurves from numbered asteroids.

The WASP Project and SuperWASP Camera

The WASP project and infrastructure supporting the SuperWASP Facility are described. As the instrument, reduction pipeline and archive system are now fully operative we expect the system to have a major impact in the discovery of bright exo-planet candidates as well in more general variable star projects.

SuperWASP-North extrasolar planet candidates: candidates from fields 17h

We have performed photometric observations of nearly seven million stars with 8 <V <15 with the SuperWASP-North instrument from La Palma between 2004 May to September. Fields in the right ascension range 17-18h, yielding over 185000 stars with sufficient quality data, have been searched for transits using a modified box least-squares (BLS) algorithm. We find a total of 58 initial transiting candidates which have high signal-to-noise ratio in the BLS, show multiple transit-like dips and have passed visual inspection. Analysis of the blending and the inferred planetary radii for these candidates leave, a total of seven transiting planet candidates which pass all the tests plus four which pass the majority. We discuss the derived parameters for these candidates and their properties and comment on the implications for future transit searches.

SuperWASP-N extrasolar planet candidates between 18 <RA <21h

The SuperWASP-I (Wide Angle Search for Planets-I) instrument observed 6.7 million stars between 8 and 15mag from La Palma during the 2004 May-September season. Our transit-hunting algorithm selected 11626 objects from the 184442 stars within the RA (right ascension) range 18-21h. We describe our thorough selection procedure whereby catalogue information is exploited along with careful study of the SuperWASP data to filter out, as far as possible, transit mimics. We have identified 35 candidates which we recommend for follow-up observations.

SuperWASP-North extrasolar planet candidates between 3h <RA <6h

The Wide Angle Search for Planets (WASP) photometrically surveys a large number of nearby stars to uncover candidate extrasolar planet systems by virtue of small-amplitude light curve dips on a

SuperWASP-N extrasolar planet candidates from fields 06h

TheWide Angle Search for Planets (WASP) survey currently operates two installations, designated SuperWASP-N and SuperWASP-S, located in the Northern and Southern hemispheres, respectively. These installations are designed to provide high time-resolution photometry for the purpose of detecting transiting extrasolar planets, asteroids, and transient events. Here, we present results from a transit-hunting observing campaign using SuperWASP-N covering a right ascension (RA) range of 06h < RA < 16h. This paper represents the fifth and final in the series of transit candidates released from the 2004 observing season. In total, 729 335 stars from 33 fields were monitored with 130 566 having sufficient precision to be scanned for transit signatures. Using a robust transit detection algorithm and selection criteria, six stars were found to have events consistent with the signature of a transiting extrasolar planet based on the photometry, including the known transiting planet XO-1b. These transit candidates are presented here along with discussion of follow-up observations and the expected number of candidates in relation to the overall observing strategy.

WASP-3b: a strongly irradiated transiting gas-giant planet

We report the discovery of WASP-3b, the third transiting exoplanet to be discovered by the WASP and SOPHIE collaboration. WASP-3b transits its host star USNO-B1.01256-0285133 every 1.846834 +/- 0.000002 d. Our high-precision radial velocity measurements present a variation with amplitude characteristic of a planetary-mass companion and in phase with the light curve. Adaptive optics imaging shows no evidence for nearby stellar companions, and line-bisector analysis excludes faint, unresolved binarity and stellar activity as the cause of the radial velocity variations. We make a preliminary spectroscopic analysis of the host star and find it to have Teff = 6400 +/- 100K and log g = 4.25 +/- 0.05 which suggests it is most likely an unevolved main-sequence star of spectral type F7-8V. Our simultaneous modelling of the transit photometry and reflex motion of the host leads us to derive a mass of 1.76+0.08-0.14 MJ and radius 1.31+0.07-0.14 RJ for WASP-3b. The proximity and relative temperature of the host star suggests that WASP-3b is one of the hottest exoplanets known, and thus has the potential to place stringent constraints on exoplanet atmospheric models.

WASP-4b: A 12th magnitude transiting hot Jupiter in the southern hemisphere

We report the discovery of WASP-4b, a large transiting gas-giant planet with an orbital period of 1.34 days. This is the first planet to be discovered by the SuperWASP-South observatory and CORALIE collaboration and the first planet orbiting a star brighter than 16th magnitude to be discovered in the southern hemisphere. A simultaneous fit to high-quality light curves and precision radial velocity measurements leads to a planetary mass of 1.22(-0.08)(+0.09) M-Jup and a planetary radius of 1.42(-0.04)(+0.07) R-Jup. The host star is USNO-B1.0 0479-0948995, a G7 V star of visual magnitude 12.5. As a result of the short orbital period, the predicted surface temperature of the planet is 1761 K, making it an ideal candidate for detections of the secondary eclipse at infrared wavelengths.

The 0.5M(J) transiting exoplanet WASP-13b

We report the discovery of WASP-13b, a low-mass M-p = 0.46(-0.05)(+0.06) M-J transiting exoplanet with an orbital period of 4.35298 +/- 0.00004 days. The transit has a depth of 9 mmag, and although our follow-up photometry does not allow us to constrain the impact parameter well (0 <b <0.46), with radius in the range R-p similar to 1.06-1.21 R-J the location of WASP-13b in the mass-radius plane is nevertheless consistent with H/He-dominated, irradiated, low core mass and core-free theoretical models. The G1V host star is similar to the Sun in mass (M-* = 1.03(-0.09)(+0.11) M-circle dot) and metallicity ([M/H] = 0.0 +/- 0.2), but is possibly older (8.5(-4.9)(+5.5) Gyr).

WASP-14b: 7.3 M-J transiting planet in an eccentric orbit

We report the discovery of a 7.3 M-J exoplanet WASP-14b, one of the most massive transiting exoplanets observed to date. The planet orbits the 10th-magnitude F5V star USNO-B1 11118-0262485 with a period of 2.243 752 d and orbital eccentricity e = 0.09. A simultaneous fit of the transit light curve and radial velocity measurements yields a planetary mass of 7.3 +/- 0.5 M-J and a radius of 1.28 +/- 0.08 R-J. This leads to a mean density of about 4.6 g cm(-3) making it the densest transiting exoplanets yet found at an orbital period less than 3 d. We estimate this system to be at a distance of 160 +/- 20 pc. Spectral analysis of the host star reveals a temperature of 6475 +/- 100 K, log g = 4.07 cm s(-2) and v sin i = 4.9 +/- 1.0 km s(-1), and also a high lithium abundance, log N(Li) = 2.84 +/- 0.05. The stellar density, effective temperature and rotation rate suggest an age for the system of about 0.5-1.0 Gyr.