http://hdl.handle.net/2117/1132 2013-05-24T04:19:03Z http://hdl.handle.net/2117/6777 Title: Classification of local stellar populations: the improved MEMPHIS algorithm - Part II Authors: Cubarsí Morera, Rafael; Alcobé López, Santiago Abstract: Discontinuities of the local velocity distribution which are associated with stellar populations are studied from the improved statistical method MEMPHIS (Maximum Entropy of the Mixture Probability from HIerarchical Segregation), by combining a sampling parameter, optimisation of the mixture approach, and maximum partition entropy of populations composing the stellar sample. The sampling parameter is associated with isolating integrals of the star motion and it is used to build a hierarchical family of subsamples. An accurate characterisation of the entropy graph is given where a local maximum of entropy takes place simultaneously with a local minimum 2 error. By working from different sampling parameters the method is applied to samples from HIPPARCOS and Geneva-Copenhagen survey (GCS) to obtain kinematic parameters and mixture proportions of thin disk, thick disk and halo. The sampling parameter P = |(U, V,W)|, absolute heliocentric velocity, allows to build an optimal subsample containing thin and thick disk stars, by leaving aside most of the halo population. The sampling parameter P = |W|, absolute perpendicular velocity, is able to build an optimal subsample containing a mixture of total disk and halo stars, although it does not allow an optimal segregation of thin and thick disks. Other sampling parameters like P = |(U,W)| or P = |V | are found to be less population informative. By comparing both samples, HIPPARCOS provides more accurate estimates for thick disk and halo, while GCS does for the total disk. In particular, the radial velocity dispersion of the halo fits perfectly into the empirical Titius-Bode like law U = 6.6 ( 4 3 )3n+2, which was previously proposed for discrete kinematic components, where the values n = 0, 1, 2, 3 stands for early-type stars, thin disk, thick disk, and halo populations. Population statistics are used to segregate thin disk, thick disk, and halo, and to obtain a more accurate bayesian estimation of the population fractions. 2010-03-23T11:10:08Z http://hdl.handle.net/2117/6775 Title: Partition entropy and chi-squared error: the improved MEMPHIS algorithm - Part I Authors: Cubarsí Morera, Rafael; Alcobé López, Santiago Abstract: The entropy of the population partition is studied as a function of the sampling parameter, so that within a particular interval of its graph, the plateau region, it is possible to get a stable estimation of the mixture parameters. The optimal estimation is associated with a local maximum of entropy. Alter natively, the $\chi^2$ error of the mixture approach may also be used to obtain an optimal segregation. The relationship between the fitting error and the population entropy has been analysed in detail. We have proved that, by using an appropriate sampling parameter, within a plateau region of the entropy graph, a local entropy maximum takes place simultaneously with a local minimum of the $\chi^2$ error. Therefore, the combined statistical method provides the best approximation mixture, as well as the less informative partiti on, to estimate the kinematic parameters of populations. 2010-03-23T10:56:41Z http://hdl.handle.net/2117/6773 Title: Structure of the velocity distribution of the Galactic disc: a maximum entropy statistical approach - Part I Authors: Cubarsí Morera, Rafael Abstract: The maximum entropy approach is proposed to describe the local structures of the veloc- ity distribution, which are collected through its sample moments. The method is used with several samples from the HIPPARCOS and Geneva-Copenhagen survey catalogues. For the large-scale distribution, the phase density function may be obtained by fitting moments up to sixth order as a product of two exponential functions, one giving a background ellipsoidal shape of the distribution and the other accounting for the skewness and for the slight shift in the ellipsoidal isocontours in terms of the rotation velocity. The small-scale distribution can be deduced from truncated distributions, such as velocity-bounded samples with |V| ≤ 51 km s−1, which contain a complex mixture of early-type and young disc stars. By fitting up to ten-order moments, the maximum entropy approach gives a realistic portrait of actual asymmetries, showing a clear bimodal pattern: (i) around the Hyades-Pleiades stream, with negative radial mean velocity and (ii) around the Sirius-UMa stream, with slightly positive radial mean velocity. The “U-anomaly” along the radial direction is estimated straightfor- wardly 30 − 35 km s−1 from the contour plots. 2010-03-23T10:45:48Z http://hdl.handle.net/2117/6700 Title: Small-scale structure of the disc velocity distribution. A maximum entropy statistical approach - Part II Authors: Cubarsí Morera, Rafael Abstract: Among metallicity, colour, and other star properties, the eccentricity of the star’s orbit behaves as a very good sampling parameter to find a more detailed structure for the disc velocity distribution, allowing distinctions between different eccentricity layers. For subsam- ples with eccentricities e < 0.15, star velocities are approximately symmetrically distributed around the LSR in the radial direction, with a dearth of stars at the LSR. For e = 0.15, the core distribution of the thin disc is supported by two major stellar groups with opposite radial velocities. Several simulations confirm that such a double-peaked distribution comes from the lognormal distribution of the velocity amplitudes. For maximum eccentricity 0.3 and maximum distance to the Galactic plane 0.5 kpc a representative thin disc sample is obtained. An explanation of the apparent vertex deviation of the disc from the swinging of those major kinematic groups around the LSR is possible, which predicts a continuously changing orientation of the disc’s pseudo ellipsoid. 2010-03-18T12:49:37Z http://hdl.handle.net/2117/3046 Title: On the maximum entropy and the problem of moments: an application to stellar kinematics Authors: Cubarsí Morera, Rafael Abstract: The maximum entropy approach is used to solve the classical moment problem of stellar kinematics. If an extended set of moments is available, the current method provides a linear estimation algorithm, which is given by a Gramian system of equations, that leads to a fast and suitable estimation of the velocity distribution. In particular, it can be used as an alternative approach for modelling multimodal distributions that can not be described through gaussian mixtures. 2009-08-24T09:04:26Z http://hdl.handle.net/2117/1244 Title: Closure of the stellar hydrodynamic equations for Gaussian and ellipsoidal velocity distributions Authors: Cubarsí Morera, Rafael Abstract: The closure conditions, which make a finite set of moment equations equivalent to the collisionless Boltzmann equation, are investigated for Gaussian and ellipsoidal velocity distributions working from the com- plete mathematical expression for the nth-order stellar hydrodynamic equation, which was explicitly obtained depending on the comoving mo- ments in a previous paper. First, for a Schwarzschild distribution, it is proved that the whole set of hydrodynamic equations is reduced to the equations of orders n = 0,1,2,3, owing to the recurrent form of the central moments. Furthermore, the equations of order n = 2 and n = 3 become closure conditions for higher even- and odd-order equations, re- spectively. An arbitrary quadratic function in the peculiar velocities, the generalised Schwarzschild distribution, is also investigated. Analogous closure conditions could be obtained from a similar recurrence law for central moments, but an alternative procedure is preferred, which con- sists in to expand a generalised ellipsoidal function as a power series of Schwarzschild distributions with the same mean. Then, due to the linear nature of the problem, the equivalence between the moment equations and the system of equations that Chandrasekhar had obtained working from the collisionless Boltzmann equation is borne out. 2007-10-11T18:30:08Z http://hdl.handle.net/2117/1242 Title: The complete form of moment equations of stellar dynamics Authors: Cubarsí Morera, Rafael Abstract: The exact mathematical expression for an arbitrary nth-order stellar hydrodynamic equation is explicitly obtained depending on the central moments of the velocity distribution. In such a form the equations are physically meaningful, since they can be compared with the ordinary hy- drodynamic equations of compressible, viscous fluids. The equations are deduced without any particular assumptions about symmetries, steadi- ness, or particular kinematic behaviours, so that they can be used in their complete form, and for any order, in future works with improved observational data. Also, in order to work with a finite number of equa- tions and unknowns, which would provide a dynamic model for the stel- lar system, the nth-order equation is needed to investigate in a more general way the closure conditions, which may be expressed in terms of velocity distribution statistics, as it is shown in a case example. 2007-10-11T18:04:39Z http://hdl.handle.net/2117/969 Title: Study of several interpolation schemes to provide ionospheric corrections for navigation Authors: Orús Pérez, Raül; García Fernández, Miquel; Prats Menéndez, Xavier; Hernández Pajares, Manuel; Juan, Miguel Abstract: Since the development of space based geodesic techniques, the increasing of the positioning accuracy has been a major goal. In this context, the effect of the ionosphere has been a key issue to be taken into account to improve the navigation results obtained using several types of receivers: from dual frequency phase receivers at distances greater than tens of kilometres of the nearest fixed site to single frequency code receivers. To overcome this problem, it is necessary either an accurate modelling of the ionosphere at the fixed stations and an optimum interpolation scheme for the rover receiver. This approach is either valid for single frequency users or rovers using dual frequency phase receiver. The current work studies the performance of different interpolation schemes such as linear interpolation and kriging, which can be implemented in a rover receiver in order to interpolate either the Slant Total Electron Content (from now on STEC) or the Double Differenced STEC from the transmitted corrections that are computed at the fixed stations. 2007-05-10T09:02:21Z