High inclination orbits in the secular quadrupolar three-body problem

The Lidov-Kozai mechanism allows a body to periodically exchange its eccentricity with inclination. It was first discussed in the framework of the quadrupolar secular restricted three-body problem, where the massless particle is the inner body, and later extended to the quadrupolar secular nonrestricted three body problem. In this paper, we propose a different point of view on the problem by looking first at the restricted problem where the massless particle is the outer body. In this situation, equilibria at high mutual inclination appear, which correspond to the population of stable particles that Verrier & Evans (2008,2009) find in stable, high inclination circumbinary orbits around one of the components of the quadruple star HD 98800. We provide a simple analytical framework using a vectorial formalism for these situations. We also look at the evolution of these high inclination equilibria in the non restricted case.Comment: 11 pages, 6 figures. Accepted by MNRAS 2009 September 1

Luminosity Functions of XMM-LSS C1 Galaxy Clusters

CFHTLS optical photometry has been used to study the galaxy luminosity functions of 14 X-ray selected clusters from the XMM-LSS survey. These are mostly groups and poor clusters, with masses (M_{500}) in the range 0.6 to 19x10 ^{13} M_solar and redshifts 0.05-0.61. Hence these are some of the highest redshift X-ray selected groups to have been studied. Lower and upper colour cuts were used to determine cluster members. We derive individual luminosity functions (LFs) for all clusters as well as redshift-stacked and temperature-stacked LFs in three filters, g', r' and z', down to M=-14.5. All LFs were fitted by Schechter functions which constrained the faint-end slope, alpha, but did not always fit well to the bright end. Derived values of alpha ranged from -1.03 to as steep as -2.1. We find no evidence for upturns at faint magnitudes. Evolution in alpha was apparent in all bands: it becomes shallower with increasing redshift; for example, in the z' band it flattened from -1.75 at low redshift to -1.22 in the redshift range z=0.43-0.61. Eight of our systems lie at z~0.3, and we combine these to generate a galaxy LF in three colours for X-ray selected groups and poor clusters at redshift 0.3. We find that at z~0.3 alpha is steeper (-1.67) in the green (g') band than it is (-1.30) in the red (z') band. This colour trend disappears at low redshift, which we attribute to reddening of faint blue galaxies from z~0.3 to z~0. We also calculated the total optical luminosity and found it to correlate strongly with X-ray luminosity (L_X proportional to L_OPT^(2.1)), and also with ICM temperature (L_OPT proportional to T^(1.62)), consistent with expectations for self-similar clusters with constant mass-to-light ratio. We did not find any convincing correlation of Schechter parameters with mean cluster temperature.Comment: 23 pages, 17 figure

Importance of Baseline Prognostic Factors With Increasing Time Since Initiation of Highly Active Antiretroviral Therapy: Collaborative Analysis of Cohorts of HIV-1-Infected Patients

Background: The extent to which the prognosis for AIDS and death of patients initiating highly active antiretroviral therapy (HAART) continues to be affected by their characteristics at the time of initiation (baseline) is unclear. Methods: We analyzed data on 20,379 treatment-naive HIV-1- infected adults who started HAART in 1 of 12 cohort studies in Europe and North America (61,798 person-years of follow-up, 1844 AIDS events, and 1005 deaths). Results: Although baseline CD4 cell count became less prognostic with time, individuals with a baseline CD4 count 350 cells/μL (hazard ratio for AIDS = 2.3, 95% confidence interval [CI]: 1.0 to 2.3; mortality hazard ratio = 2.5, 95% CI: 1.2 to 5.5, 4 to 6 years after starting HAART). Rates of AIDS were persistently higher in individuals who had experienced an AIDS event before starting HAART. Individuals with presumed transmission by means of injection drug use experienced substantially higher rates of AIDS and death than other individuals throughout follow-up (AIDS hazard ratio = 1.6, 95% CI: 0.8 to 3.0; mortality hazard ratio = 3.5, 95% CI: 2.2 to 5.5, 4 to 6 years after starting HAART). Conclusions: Compared with other patient groups, injection drug users and patients with advanced immunodeficiency at baseline experience substantially increased rates of AIDS and death up to 6 years after starting HAART