The discrete fragmentation equations : semigroups, compactness and asynchronous exponential growth

In this paper we present a class of fragmentation semigroups which are compact in a scale of spaces defined in terms of finite higher moments. We use this compactness result to analyse the long time behaviour of such semigroups and, in particular, to prove that they have the asynchronous growth property. We note that, despite compactness, this growth property is not automatic as the fragmentation semigroups are not irreducible

The Anomaly in the Candidate Microlensing Event PA-99-N2

The lightcurve of PA-99-N2, one of the recently announced microlensing candidates towards M31, shows small deviations from the standard Paczynski form. We explore a number of possible explanations, including correlations with the seeing, the parallax effect and a binary lens. We find that the observations are consistent with an unresolved RGB or AGB star in M31 being microlensed by a binary lens. We find that the best fit binary lens mass ratio is about one hundredth, which is one of most extreme values found for a binary lens so far. If both the source and lens lie in the M31 disk, then the standard M31 model predicts the probable mass range of the system to be 0.02-3.6 solar masses (95 % confidence limit). In this scenario, the mass of the secondary component is therefore likely to be below the hydrogen-burning limit. On the other hand, if a compact halo object in M31 is lensing a disk or spheroid source, then the total lens mass is likely to lie between 0.09-32 solar masses, which is consistent with the primary being a stellar remnant and the secondary a low mass star or brown dwarf. The optical depth (or alternatively the differential rate) along the line of sight toward the event indicates that a halo lens is more likely than a stellar lens provided that dark compact objects comprise no less than 15 per cent (or 5 per cent) of haloes.Comment: Latex, 23 pages, 9 figures, in press at The Astrophysical Journa

The hidden burden of adult allergic rhinitis : UK healthcare resource utilisation survey

Funding Funding for this survey was provided by Meda Pharma.Peer reviewedPublisher PD

The POINT-AGAPE survey II: An Unrestricted Search for Microlensing Events towards M31

An automated search is carried out for microlensing events using a catalogue of 44554 variable superpixel lightcurves derived from our three-year monitoring program of M31. Each step of our candidate selection is objective and reproducible by a computer. Our search is unrestricted, in the sense that it has no explicit timescale cut. So, it must overcome the awkward problem of distinguishing long-timescale microlensing events from long-period stellar variables. The basis of the selection algorithm is the fitting of the superpixel lightcurves to two different theoretical models, using variable star and blended microlensing templates. Only if microlensing is preferred is an event retained as a possible candidate. Further cuts are made with regard to (i) sampling, (ii) goodness of fit of the peak to a Paczynski curve, (iii) consistency of the microlensing hypothesis with the absence of a resolved source, (iv) achromaticity, (v) position in the colour-magnitude diagram and (vi) signal-to-noise ratio. Our results are reported in terms of first-level candidates, which are the most trustworthy, and second-level candidates, which are possible microlensing but have lower signal-to-noise and are more questionable. The pipeline leaves just 3 first-level candidates, all of which have very short full-width half-maximum timescale (<5 days) and 3 second-level candidates, which have timescales of 31, 36 and 51 days respectively. We also show 16 third-level lightcurves, as an illustration of the events that just fail the threshold for designation as microlensing candidates. They are almost certainly mainly variable stars. Two of the 3 first-level candidates correspond to known events (PA 00-S3 and PA 00-S4) already reported by the POINT-AGAPE project. The remaining first-level candidate is new.Comment: 22 pages, 18 figures, MNRAS, to appea

The POINT-AGAPE survey — II. An unrestricted search for microlensing events towards M31

An automated search is carried out for microlensing events using a catalogue of 44 554 variable superpixel light curves derived from our 3-yr monitoring programme of M31. Each step of our candidate selection is objective and reproducible by a computer. Our search is unrestricted, in the sense that it has no explicit time-scale cut. So, it must overcome the awkward problem of distinguishing long time-scale microlensing events from long-period stellar variables. The basis of the selection algorithm is the fitting of the superpixel light curves to two different theoretical models, using variable star and blended microlensing templates. Only if microlensing is preferred is an event retained as a possible candidate. Further cuts are made with regard to: (i) sampling, (ii) goodness of fit of the peak to a Paczyński curve, (iii) consistency of the microlensing hypothesis with the absence of a resolved source, (iv) achromaticity, (v) position in the colour-magnitude diagram and (vi) signal-to-noise ratio. Our results are reported in terms of first-level candidates, which are the most trustworthy, and second-level candidates, which are possible microlensing events but have a lower signal-to-noise ratio and are more questionable. The pipeline leaves just three first-level candidates, all of which have very short full-width at half-maximum time-scales (t1/2 < 5 d) and three second-level candidates, which have time-scales of t1/2 = 31, 36 and 51 d. We also show 16 third-level light curves, as an illustration of the events that just fail the threshold for designation as microlensing candidates. They are almost certainly mainly variable stars. Two of the three first-level candidates correspond to known events (PA 00-S3 and 00-S4) already reported by the POINT-AGAPE project. The remaining first-level candidate is new. This algorithm does not find short time-scale events that are contaminated with flux from nearby variable stars (such as PA 99-N1

The POINT-AGAPE Survey - I. The variable stars in M31

For the purposes of identifying microlensing events, the POINT-AGAPE collaboration has been monitoring the Andromeda galaxy (M31) for three seasons (1999-2001) with the Wide Field Camera on the Isaac Newton Telescope. In each season, data are taken for one hour per night for roughly 60 nights during the six months that M31 is visible. The two 33 × 33 arcmin2 fields of view straddle the central bulge, northwards and southwards. We have calculated the locations, periods and brightness of 35 414 variable stars in M31 as a by-product of the microlensing search. The variables are classified according to their period and brightness. Rough correspondences with classical types of variable star (such as Population I and II Cepheids, Miras and semiregular long-period variables) are established. The spatial distribution of Population I Cepheids is clearly associated with the spiral arms, while the central concentration of the Miras and long-period variables varies noticeably, the brighter and the shorter period Miras being much more centrally concentrated. A crucial role in the microlensing experiment is played by the asymmetry signal - the excess of events expected in the southern or more distant fields as measured against those in the northern or nearer fields. It was initially assumed that the variable star populations in M31 would be symmetric with respect to the major axis, and thus variable stars would not be a serious contaminant for measuring the microlensing asymmetry signal. We demonstrate that this assumption is not correct. All the variable star distributions are asymmetric primarily because of the effects of differential extinction associated with the dust lanes. The size and direction of the asymmetry of the variable stars is measured as a function of period and brightness. The implications of this discovery for the successful completion of the microlensing experiments towards M31 are discusse

On the Possibility of Observing the Shapiro Effect for Pulsars in Globular Clusters

For pulsars in globular clusters, we suggest using observations of the relativistic time delay of their radiation in the gravitational eld of a massive body (the Shapiro effect) located close to the line of sight to detect and identify invisible compact objects and to study the distribution of both visible and dark matter in globular clusters and various components of the Galaxy. We have derived the dependences of the event probability on the Galactic latitude and longitude of sources for two models of the mass distribution in the Galaxy: the classical Bahcall-Soneira model and the more recent Dehnen-Binney model. Using three globular clusters (M15, 47 Tuc, Terzan 5) as an example, we show that the ratios of the probability of the events due to the passages of massive Galactic objects close to the line of sight to the parameter f2 for pulsars in the globular clusters 47 Tuc and M15 are comparable to those for close passages of massive objects in the clusters themselves and are considerably higher than those for the cluster Terzan 5. We have estimated the rates of such events. We have determined the number of objects near the line of sight toward the pulsar that can produce a modulation of its pulse arrival times characteristic of the effect under consideration; the population of brown dwarfs in the Galactic disk, whose concentration is comparable to that of the disk stars, has been taken into account for the first time.Comment: 26 pages, 9 figure

Classical novae from the POINT-AGAPE microlensing survey of M31 -- I. The nova catalogue

The POINT-AGAPE survey is an optical search for gravitational microlensing events towards the Andromeda Galaxy (M31). As well as microlensing, the survey is sensitive to many different classes of variable stars and transients. Here we describe the automated detection and selection pipeline used to identify M31 classical novae (CNe) and we present the resulting catalogue of 20 CN candidates observed over three seasons. CNe are observed both in the bulge region as well as over a wide area of the M31 disk. Nine of the CNe are caught during the final rise phase and all are well sampled in at least two colours. The excellent light-curve coverage has allowed us to detect and classify CNe over a wide range of speed class, from very fast to very slow. Among the light-curves is a moderately fast CN exhibiting entry into a deep transition minimum, followed by its final decline. We have also observed in detail a very slow CN which faded by only 0.01 mag day$^{-1}$ over a 150 day period. We detect other interesting variable objects, including one of the longest period and most luminous Mira variables. The CN catalogue constitutes a uniquely well-sampled and objectively-selected data set with which to study the statistical properties of classical novae in M31, such as the global nova rate, the reliability of novae as standard-candle distance indicators and the dependence of the nova population on stellar environment. The findings of this statistical study will be reported in a follow-up paper.Comment: 21 pages, 13 figures, re-submitted for publication in MNRAS, typos corrected, references updated, figures 5-9 made cleare

The Minimal Supersymmetric Standard Model: Group Summary Report

CONTENTS: 1. Synopsis, 2. The MSSM Spectrum, 3. The Physical Parameters, 4. Higgs Boson Production and Decays, 5. SUSY Particle Production and Decays, 6. Experimental Bounds on SUSY Particle Masses, 7. References.Comment: 121 pages, latex + epsfig, graphicx, axodraw, Report of the MSSM working group for the Workshop "GDR-Supersym\'etrie",France. Rep. PM/98-4

Classical novae from the POINT-AGAPE microlensing survey of M31 - II. Rate and statistical characteristics of the nova population

The POINT-AGAPE (Pixel-lensing Observations with the Isaac Newton Telescope-Andromeda Galaxy Amplified Pixels Experiment) survey is an optical search for gravitational microlensing events towards the Andromeda galaxy (M31). As well as microlensing, the survey is sensitive to many different classes of variable stars and transients. In our first paper of this series, we reported the detection of 20 classical novae (CNe) observed in Sloan r′ and i′ passbands. An analysis of the maximum magnitude versus rate of decline (MMRD) relationship in M31 is performed using the resulting POINT-AGAPE CN catalogue. Within the limits of the uncertainties of extinction internal to M31, good fits are produced to the MMRD in two filters. The MMRD calibration is the first to be performed for Sloan r′ and i′ filters. However, we are unable to verify that novae have the same absolute magnitude 15 d after peak (the t15 relationship), nor any similar relationship for either Sloan filter. The subsequent analysis of the automated pipeline has provided us with the most thorough knowledge of the completeness of a CN survey to date. In addition, the large field of view of the survey has permitted us to probe the outburst rate well into the galactic disc, unlike previous CCD imaging surveys. Using this analysis, we are able to probe the CN distribution of M31 and evaluate the global nova rate. Using models of the galactic surface brightness of M31, we show that the observed CN distribution consists of a separate bulge and disc population. We also show that the M31 bulge CN eruption rate per unit r′ flux is more than five times greater than that of the disc. Through a combination of the completeness, M31 surface brightness model and our M31 CN eruption model, we deduce a global M31 CN rate of 65+16−15 yr−1, a value much higher than found by previous surveys. Using the global rate, we derive a M31 bulge rate of 38+15−12 yr−1 and a disc rate of 27+19−15 yr−1. Given our understanding of the completeness and an analysis of other sources of error, we conclude that the true global nova rate of M31 is at least 50 per cent higher than was previously thought and this has consequent implications for the presumed CN rate in the Milky Way. We deduce a Galactic bulge rate of 14+6−5 yr−1, a disc rate of 20+14−11 yr−1 and a global Galactic rate of 34+15−12 yr−1, consistent with the Galactic global rate derived elsewhere by independent method