The portrait of Malin 2: a case study of a giant low surface brightness galaxy

The low surface brightness disc galaxy Malin2 challenges the standard theory of galaxy evolution by its enormous total mass ~2 10^12 Ms which must have been formed without recent major merger events. The aim of our work is to create a coherent picture of this exotic object by using the new optical multicolor photometric and spectroscopic observations at Apache Point Observatory as well as archival datasets from Gemini and wide-field surveys. We performed the Malin2 mass modelling, estimated the contribution of the host dark halo and found that it had acquired its low central density and the huge isothermal sphere core radius before the disc subsystem was formed. Our spectroscopic data analysis reveals complex kinematics of stars and gas in the very inner region. We measured the oxygen abundance in several clumps and concluded that the gas metallicity decreases from the solar value in the centre to a half of that at 20-30 kpc. We found a small satellite and measured its mass (1/500 of the host galaxy) and gas metallicity. One of the unique properties of Malin2 turned to be the apparent imbalance of ISM: the molecular gas is in excess with respect to the atomic gas for given values of the gas equilibrium turbulent pressure. We explain this imbalance by the presence of a significant portion of the dark gas not observable in CO and the Hi 21 cm lines. We also show that the depletion time of the observed molecular gas traced by CO is nearly the same as in normal galaxies. Our modelling of the UV-to-optical spectral energy distribution favours the exponentially declined SFH over a single-burst scenario. We argue that the massive and rarefied dark halo which had formed before the disc component well describes all the observed properties of Malin2 and there is no need to assume additional catastrophic scenarios proposed previously to explain the origin of giant LSB galaxies. [Abbreviated]Comment: 17 pages, 10 figures, accepted for publication in MNRA

Relaxation time spectrum of low-energy excitations in one- and two-dimensional materials with charge or spin density waves

The long-time thermal relaxation of (TMTTF)$_2$Br, Sr$_{14}$Cu$_{24}$O$_{41}$ and Sr$_2$Ca$_{12}$Cu$_{24}$O$_{41}$ single crystals at temperatures below 1 K and magnetic field up to 10 T is investigated. The data allow us to determine the relaxation time spectrum of the low energy excitations caused by the charge-density wave (CDW) or spin-density wave (SDW). The relaxation time is mainly determined by a thermal activated process for all investigated materials. The maximum relaxation time increases with increasing magnetic field. The distribution of barrier heights corresponds to one or two Gaussian functions. The doping of Sr$_{14-x}$Ca$_{x}$Cu$_{24}$O$_{41}$ with Ca leads to a drastic shift of the relaxation time spectrum to longer time. The maximum relaxation time changes from 50 s (x = 0) to 3000 s (x = 12) at 0.1 K and 10 T. The observed thermal relaxation at x=12 clearly indicates the formation of the SDW ground state at low temperatures

Lie symmetry analysis and exact solutions of the quasi-geostrophic two-layer problem

The quasi-geostrophic two-layer model is of superior interest in dynamic meteorology since it is one of the easiest ways to study baroclinic processes in geophysical fluid dynamics. The complete set of point symmetries of the two-layer equations is determined. An optimal set of one- and two-dimensional inequivalent subalgebras of the maximal Lie invariance algebra is constructed. On the basis of these subalgebras we exhaustively carry out group-invariant reduction and compute various classes of exact solutions. Where possible, reference to the physical meaning of the exact solutions is given. In particular, the well-known baroclinic Rossby wave solutions in the two-layer model are rediscovered.Comment: Extended version, 24 pages, 1 figur