We present a mathematical method to statistically decouple the effects of unknown inclination angles on the mass distribution of exoplanets that have been discovered using radial-velocity techniques. The method is based on the distribution of the pro
duct of two random variables. Thus, if one assumes a true mass distribution, the method makes it possible to recover the observed distribution. We compare our prediction with available radial-velocity data. Assuming the true mass function is described by a power-law, the minimum mass function that we recover proves a good fit to the observed distribution at both mass ends. In particular, it provides an alternative explanation for the observed low-mass decline, usually explained as sample incompleteness. In addition, the peak observed near the the low-mass end arises naturally in the predicted distribution as a consequence of imposing a low-mass cutoff in the true-distribution. If the low-mass bins below 0.02 M_J are complete, then the mass distribution in this regime is heavily affected by the small fraction of lowly inclined interlopers that are actually more massive companions. Finally, we also present evidence that the exoplanet mass distribution changes form towards low-mass, implying that a single power law may not adequately describe the sample population.
This paper reports an investigation on the phase diagram and compressibility of wolframite-type tungstates by means of x-ray powder diffraction and absorption in a diamond-anvil cell and ab initio calculations. The diffraction experiments show that m
onoclinic wolframite-type MgWO4 suffers at least two phase transitions, the first one being to a triclinic polymorph with a structure similar to that of CuWO4 and FeMoO4-II. The onset of each transition is detected at 17.1 and 31 GPa. In ZnWO4 the onset of the monoclinic-triclinic transition has been also found at 15.1 GPa. These findings are supported by density-functional theory calculations, which predict the occurrence of additional transitions upon further compression. Calculations have been also performed for wolframite-type MnWO4, which is found to have an antiferromagnetic configuration. In addition, x-ray absorption and diffraction experiments as well as calculations reveal details of the local-atomic compression in the studied compounds. In particular, below the transition pressure the ZnO6 and equivalent polyhedra tend to become more regular, whereas the WO6 octahedra remain almost unchanged. Fitting the pressure-volume data we obtained the equation of state for the low-pressure phase of MgWO4 and ZnWO4. These and previous results on MnWO4 and CdWO4 are compared with the calculations, being the compressibility of wolframite-type tungstates systematically discussed. Finally Raman spectroscopy measurements and lattice dynamics calculations are presented for MgWO4.
Based on recent results on the frequency of MgII absorption line systems in the QSO behind RCS clusters survey (QbC), we analyse the effects of the cluster environment on the sizes of baryonic haloes around galaxies. We use two independent models, i)
an empirical halo occupation model which fits current measurements of the clustering and luminosity function of galaxies at low and high redshifts, and ii) the GALFORM semi-analytic model of galaxy formation, which follows the evolution of the galaxy population from first principles, adjusted to match the statistics of low and high redshift galaxies. In both models we constrain the MgII halo sizes of field and cluster galaxies using observational results on the observed MgII statistics. Our results for the field are in good agreement with previous works, indicating a typical mgii halo size of $r_MgII ~ 50h_71^-1kpc in the semi-analytic model, and slightly lower in the halo occupation number approach. For the cluster environment, we find that both models require a median MgII halo size of r_MgII< 10h_71^-1kpc in order to reproduce the observed statistics on absorption line systems in clusters of galaxies. Based on the Chen & Tinker (2008) result that stronger systems occur closer to the MgII halo centre, we find that strong absorption systems in clusters of galaxies occur at roughly a fixed fraction of the cold-warm halo size out to 1h_71^-1Mpc from the cluster centres. In contrast, weaker absorption systems appear to occur at progressively shorter relative fractions of this halo as the distance to the cluster centre decreases.
