A universal velocity distribution of relaxed collisionless structures

Several general trends have been identified for equilibrated, self-gravitating collisionless systems, such as density or anisotropy profiles. These are integrated quantities which naturally depend on the underlying velocity distribution function (VDF) of the system. We study this VDF through a set of numerical simulations, which allow us to extract both the radial and the tangential VDF. We find that the shape of the VDF is universal, in the sense that it depends only on two things namely the dispersion (radial or tangential) and the local slope of the density. Both the radial and the tangential VDF's are universal for a collection of simulations, including controlled collisions with very different initial conditions, radial infall simulation, and structures formed in cosmological simulations.Comment: 13 pages, 6 figures; oversimplified analysis corrected; changed abstract and conclusions; significantly extended discussio

The velocity anisotropy - density slope relation

One can solve the Jeans equation analytically for equilibrated dark matter structures, once given two pieces of input from numerical simulations. These inputs are 1) a connection between phase-space density and radius, and 2) a connection between velocity anisotropy and density slope, the \alpha-\beta relation. The first (phase-space density v.s. radius) has already been analysed through several different simulations, however the second (\alpha-\beta relation) has not been quantified yet. We perform a large set of numerical experiments in order to quantify the slope and zero-point of the \alpha-\beta relation. We find strong indication that the relation is indeed an attractor. When combined with the assumption of phase-space being a power-law in radius, this allows us to conclude that equilibrated dark matter structures indeed have zero central velocity anisotropy \beta_0 = 0, central density slope of \alpha_0 = -0.8, and outer anisotropy of \beta_\infty = 0.5.Comment: 15 pages, 7 figure

Stellar polytropes and Navarro-Frenk-White halo models: comparison with observations

Motivated by the possible conflict between the Navarro-Frenk-White(NFW) model predictions for the dark matter contents of galactic systems and its correlation with baryonic surface density, we will explore an alternative paradigm for the description of dark matter halos. Such an alternative emerges from Tsallis' non-extensive thermodynamics applied to self-gravitating systems and leads to the so-called ``stellar polytrope'' (SP) model. We consider that this could be a better approach to real structures rather than the isothermal model, given the fact that the first one takes into account the non-extensivity of energy and entropy present in these type of systems characterized by long-range interactions. We compare a halo based on the Navarro-Frenk-White (NFW) and one which follows the SP description. Analyzing the dark matter contents estimated by means of global physical parameters of galactic disks, obtained from a sample of actual galaxies, with the ones of the unobserved dark matter halos, we conclude that the SP model is favored over the NFW model in such a comparison.Comment: 21 pages, 4 figures. Accepted for publication in the Journal of Cosmology and Astroparticle Physic

Oral contraceptive use and reproductive factors and risk of ovarian cancer in the European Prospective Investigation into Cancer and Nutrition.

BACKGROUND: It is well established that parity and use of oral contraceptives reduce the risk of ovarian cancer, but the associations with other reproductive variables are less clear. METHODS: We examined the associations of oral contraceptive use and reproductive factors with ovarian cancer risk in the European Prospective Investigation into Cancer and Nutrition. Among 327,396 eligible women, 878 developed ovarian cancer over an average of 9 years. Hazard ratios (HRs) and 95% confidence intervals (CIs) were estimated using Cox proportional hazard models stratified by centre and age, and adjusted for smoking status, body mass index, unilateral ovariectomy, simple hysterectomy, menopausal hormone therapy, and mutually adjusted for age at menarche, age at menopause, number of full-term pregnancies and duration of oral contraceptive use. RESULTS: Women who used oral contraceptives for 10 or more years had a significant 45% (HR, 0.55; 95% CI, 0.41-0.75) lower risk compared with users of 1 year or less (P-trend, <0.01). Compared with nulliparous women, parous women had a 29% (HR, 0.71; 95% CI, 0.59-0.87) lower risk, with an 8% reduction in risk for each additional pregnancy. A high age at menopause was associated with a higher risk of ovarian cancer (>52 vs ≤ 45 years: HR, 1.46; 95% CI, 1.06-1.99; P-trend, 0.02). Age at menarche, age at first full-term pregnancy, incomplete pregnancies and breastfeeding were not associated with risk. CONCLUSION: This study shows a strong protective association of oral contraceptives and parity with ovarian cancer risk, a higher risk with a late age at menopause, and no association with other reproductive factors