Superintegrability of the Tremblay-Turbiner-Winternitz quantum Hamiltonians on a plane for odd kk

In a recent FTC by Tremblay {\sl et al} (2009 {\sl J. Phys. A: Math. Theor.} {\bf 42} 205206), it has been conjectured that for any integer value of $k$, some novel exactly solvable and integrable quantum Hamiltonian $H_k$ on a plane is superintegrable and that the additional integral of motion is a $2k$th-order differential operator $Y_{2k}$. Here we demonstrate the conjecture for the infinite family of Hamiltonians $H_k$ with odd $k \ge 3$, whose first member corresponds to the three-body Calogero-Marchioro-Wolfes model after elimination of the centre-of-mass motion. Our approach is based on the construction of some $D_{2k}$-extended and invariant Hamiltonian \chh_k, which can be interpreted as a modified boson oscillator Hamiltonian. The latter is then shown to possess a $D_{2k}$-invariant integral of motion \cyy_{2k}, from which $Y_{2k}$ can be obtained by projection in the $D_{2k}$ identity representation space.Comment: 14 pages, no figure; change of title + important addition to sect. 4 + 2 more references + minor modifications; accepted by JPA as an FT

Pure-hydrogen 3D model atmospheres of cool white dwarfs

A sequence of pure-hydrogen CO5BOLD 3D model atmospheres of DA white dwarfs is presented for a surface gravity of log g = 8 and effective temperatures from 6000 to 13,000 K. We show that convective properties, such as flow velocities, characteristic granulation size and intensity contrast of the granulation patterns, change significantly over this range. We demonstrate that these 3D simulations are not sensitive to numerical parameters unlike the 1D structures that considerably depend on the mixing-length parameters. We conclude that 3D spectra can be used directly in the spectroscopic analyses of DA white dwarfs. We confirm the result of an earlier preliminary study that 3D model spectra provide a much better characterization of the mass distribution of white dwarfs and that shortcomings of the 1D mixing-length theory are responsible for the spurious high-log g determinations of cool white dwarfs. In particular, the 1D theory is unable to account for the cooling effect of the convective overshoot in the upper atmospheres.Comment: 14 pages, 17 figures, accepted for publication in Astronomy and Astrophysic

Spectroscopic analysis of DA white dwarfs with 3D model atmospheres

We present the first grid of mean three-dimensional (3D) spectra for pure-hydrogen (DA) white dwarfs based on 3D model atmospheres. We use CO5BOLD radiation-hydrodynamics 3D simulations instead of the mixing-length theory for the treatment of convection. The simulations cover the effective temperature range of 6000 < Teff (K) < 15,000 and the surface gravity range of 7 < log g < 9 where the large majority of DAs with a convective atmosphere are located. We rely on horizontally averaged 3D structures (over constant Rosseland optical depth) to compute spectra. It is demonstrated that our spectra can be smoothly connected to their 1D counterparts at higher and lower Teff where the 3D effects are small. Analytical functions are provided in order to convert spectroscopically determined 1D effective temperatures and surface gravities to 3D atmospheric parameters. We apply our improved models to well studied spectroscopic data sets from the Sloan Digital Sky Survey and the White Dwarf Catalog. We confirm that the so-called high-log g problem is not present when employing spectra and that the issue was caused by inaccuracies in the 1D mixing-length approach. The white dwarfs with a radiative and a convective atmosphere have derived mean masses that are the same within ~0.01 Msun, in much better agreement with our understanding of stellar evolution. Furthermore, the 3D atmospheric parameters are in better agreement with independent Teff and log g values from photometric and parallax measurements.Comment: 15 pages, 18 figures, 10 pages online appendix, accepted for publication in Astronomy and Astrophysic

Revisiting the Cooling Flow Problem in Galaxies, Groups, and Clusters of Galaxies

We present a study of 107 galaxies, groups, and clusters spanning ~3 orders of magnitude in mass, ~5 orders of magnitude in central galaxy star formation rate (SFR), ~4 orders of magnitude in the classical cooling rate (dM/dt) of the intracluster medium (ICM), and ~5 orders of magnitude in the central black hole accretion rate. For each system in this sample, we measure dM/dt using archival Chandra X-ray data and acquire the SFR and systematic uncertainty in the SFR by combining over 330 estimates from dozens of literature sources. With these data, we estimate the efficiency with which the ICM cools and forms stars, finding e_cool = SFR/(dM/dt) = 1.4 +/- 0.4% for systems with dM/dt > 30 Msun/yr. For these systems, we measure a slope in the SFR-dM/dt relation greater than unity, suggesting that the systems with the strongest cool cores are also cooling more efficiently. We propose that this may be related to, on average, higher black hole accretion rates in the strongest cool cores, which could influence the total amount (saturating near the Eddington rate) and dominant mode (mechanical vs radiative) of feedback. For systems with dM/dt < 30 Msun/yr, we find that the SFR and dM/dt are uncorrelated, and show that this is consistent with star formation being fueled at a low (but dominant) level by recycled ISM gas in these systems. We find an intrinsic log-normal scatter in SFR at fixed dM/dt of 0.52 +/- 0.06 dex, suggesting that cooling is tightly self-regulated over very long timescales, but can vary dramatically on short timescales. There is weak evidence that this scatter may be related to the feedback mechanism, with the scatter being minimized (~0.4 dex) in systems for which the mechanical feedback power is within a factor of two of the cooling luminosity.Comment: 16 pages, 10 figures, 6 tables. Submitted to ApJ. Comments welcome