A perturbed differential resultant based implicitization algorithm for linear DPPEs

Let \bbK be an ordinary differential field with derivation $\partial$. Let \cP be a system of $n$ linear differential polynomial parametric equations in $n-1$ differential parameters with implicit ideal \id. Given a nonzero linear differential polynomial $A$ in \id we give necessary and sufficient conditions on $A$ for \cP to be $n-1$ dimensional. We prove the existence of a linear perturbation \cP_{\phi} of \cP so that the linear complete differential resultant \dcres_{\phi} associated to \cP_{\phi} is nonzero. A nonzero linear differential polynomial in \id is obtained from the lowest degree term of \dcres_{\phi} and used to provide an implicitization algorithm for \cP

Doppler tomography of Cataclysmic Variables

The study of cataclysmic variables (CVs), and in particular of the evolution of their accretion discs throughout their different brightness states, has benefited largely from the use of indirect imaging techniques. I report on the latest results obtained from Doppler tomography of CVs concentrating mainly on results published since the 2000 Astrotomography meeting in Brussels. Emphasis is given to the spiral structures found in the accretion discs of some CVs, to the evolution of these structures throughout quiescence and outburst, and to our search for them in more systems.Comment: 4 pages, 1 figure. Accepted for publication in AN. Proceedings of the Astrotomography Joint Discussion 09 of the IAU General Assembly 2003. Uses an.cl

Dark-matter dynamical friction versus gravitational-wave emission in the evolution of compact-star binaries

The measured orbital period decay of compact-star binaries, with characteristic orbital periods $\sim 0.1$~days, is explained with very high precision by the gravitational wave (GW) emission of an inspiraling binary in vacuum. However, the binary gravitational binding energy is also affected by an usually neglected phenomenon, namely the dark matter dynamical friction (DMDF) produced by the interaction of the binary components with their respective DM gravitational wakes. The entity of this effect depends on the orbital period and on the local value of the DM density, hence on the position of the binary in the Galaxy. We evaluate the DMDF produced by three different DM profiles: the Navarro-Frenk-White (NFW), the non-singular-isothermal-sphere (NSIS) and the Ruffini-Arg\"uelles-Rueda (RAR) profile based on self-gravitating keV fermions. We first show that indeed, due to their Galactic position, the GW emission dominates over the DMDF in the NS-NS, NS-WD and WD-WD binaries for which measurements of the orbital decay exist. Then, we evaluate the conditions under which the effect of DMDF on the binary evolution becomes comparable to, or overcomes, the one of the GW emission. We find that, for instance for $1.3$--$0.2$ $M_\odot$ NS-WD, $1.3$--$1.3$~$M_\odot$ NS-NS, and $0.25$--$0.50$~$M_\odot$ WD-WD, located at 0.1~kpc, this occurs at orbital periods around 20--30 days in a NFW profile while, in a RAR profile, it occurs at about 100 days. For closer distances to the Galactic center, the DMDF effect increases and the above critical orbital periods become interestingly shorter. Finally, we also analyze the system parameters for which DMDF leads to an orbital widening instead of orbital decay. All the above imply that a direct/indirect observational verification of this effect in compact-star binaries might put strong constraints on the nature of DM and its Galactic distribution.Comment: 15 pages, 12 figures, 2 tables, accepted for publication in Phys. Rev. D, 201

Spectral atlas of dwarf novae in outburst

Up to now, only a very small number of dwarf novae have been studied during their outburst state (~30 per cent in the Northern hemisphere). In this paper we present the first comprehensive atlas of outburst spectra of dwarf novae. We study possible correlations between the emission and absorption lines seen in the spectra and some fundamental parameters of the binaries. We find that out of the 48 spectra presented, 12 systems apart from IP Peg show strong HeII in emission: SS Aur, HL CMa, TU Crt, EM Cyg, SS Cyg, EX Dra, U Gem, HX Peg, GK Per, KT Per, V893 Sco, IY UMa, and 7 others less prominently: FO And, V542 Cyg, BI Ori, TY Psc, VZ Pyx, ER UMa, and SS UMi. We conclude that these systems are good targets for finding spiral structure in their accretion discs during outburst if models of Smak (2001) and Ogilvie (2001) are correct. This is confirmed by the fact that hints of spiral asymmetries have already been found in the discs of SS Cyg, EX Dra and U Gem.Comment: 16 pages, 14 figures. To be published in MNRA