An error estimate of Gaussian Recursive Filter in 3Dvar problem

Computational kernel of the three-dimensional variational data assimilation (3D-Var) problem is a linear system, generally solved by means of an iterative method. The most costly part of each iterative step is a matrix-vector product with a very large covariance matrix having Gaussian correlation structure. This operation may be interpreted as a Gaussian convolution, that is a very expensive numerical kernel. Recursive Filters (RFs) are a well known way to approximate the Gaussian convolution and are intensively applied in the meteorology, in the oceanography and in forecast models. In this paper, we deal with an oceanographic 3D-Var data assimilation scheme, named OceanVar, where the linear system is solved by using the Conjugate Gradient (GC) method by replacing, at each step, the Gaussian convolution with RFs. Here we give theoretical issues on the discrete convolution approximation with a first order (1st-RF) and a third order (3rd-RF) recursive filters. Numerical experiments confirm given error bounds and show the benefits, in terms of accuracy and performance, of the 3-rd RF.Comment: 9 page

Reclassification of the nearest quasar pair candidate: SDSS J15244+3032 - RXS J15244+3032

We present optical spectroscopy of the nearest quasar pair listed in the 13th edition of the Veron-Cetty & Veron catalogue, i.e. the two quasars SDSS J15244+3032 and RXS J15244+3032 (redshift z~0.27, angular separation ~7 arcsec, and line-of-sight velocity difference ~1900 km/s). This system would be an optimal candidate to investigate the mutual interaction of the host galaxies with ground based optical imaging and spectroscopy. However, new optical data demonstrate that RXS J15244+3032 is indeed a star of spectral type G. This paper includes data gathered with the Asiago 1.82m telescope (Cima Ekar Observatory, Asiago, Italy).Comment: 5 pages, 2 figures, 1 table. Accepted for publication in APS

On the cool gaseous haloes of quasars

We present optical spectroscopy of projected QSO pairs to investigate the MgII and the CIV absorption features imprinted on the spectrum of the background object by the gaseous halo surrounding the foreground QSO. We observed 13 projected pairs in the redshift range 0.7<z<2.2 spanning projected separations between 60 kpc and 120 kpc. In the spectra of the background QSOs, we identify MgII intervening absorption systems associated to the foreground QSOs in 7 out of 10 pairs, and 1 absorption system out of 3 is found for CIV. The distribution of the equivalent width as a function of the impact parameter shows that, unlike the case of normal galaxies, some strong absorption systems (EWr > 1 Ang) are present also beyond a projected radius of ~70 kpc. If we take into account the mass of the galaxies as an additional parameter that influence the extent of the gaseous haloes, the distribution of the absorptions connected to the QSOs is consistent to that of galaxies. In the spectra of the foreground QSOs we do not detect any MgII absorption lines originated by the gas surrounding the QSO itself, but in 2 cases these features are present for CIV. The comparison between the absorption features observed in the transverse direction and those along the line of sight allows us to comment on the distribution of the absorbing gas and on the emission properties of the QSOs. Based on observations undertaken at the European Southern Observatory (ESO) Very Large Telescope (VLT) under Programmes 085.B-0210(A) and 086.B-0028(A).Comment: 15 pages, 3 tables, 9 figures. Accepted to be published on MNRA