Three-dimensional Dirac oscillator in a thermal bath

The thermal properties of the three-dimensional Dirac oscillator are considered. The canonical partition function is determined, and the high-temperature limit is assessed. The degeneracy of energy levels and their physical implications on the main thermodynamic functions are analyzed, revealing that these functions assume values greater than the one-dimensional case. So that at high temperatures, the limit value of the specific heat is three times bigger.Comment: 9 pages, 4 figures. Text improved, references added. Revised to match accepted version in Europhysics Letters

The dust masses of powerful radio galaxies: clues to the triggering of their activity

We use deep Herschel Space Observatory observations of a 90% complete sample of 32 intermediate-redshift 2Jy radio galaxies (0.05 < z < 0.7) to estimate the dust masses of their host galaxies and thereby investigate the triggering mechanisms for their quasar-like AGN. The dust masses derived for the radio galaxies (7.2x10^5 < M_d < 2.6x10^8 M_sun) are intermediate between those of quiescent elliptical galaxies on the one hand, and ultra luminous infrared galaxies (ULIRGs) on the other. Consistent with simple models for the co-evolution of supermassive black holes and their host galaxies, these results suggest that most of the radio galaxies represent the late time re-triggering of AGN activity via mergers between the host giant elliptical galaxies and companion galaxies with relatively low gas masses. However, a minority of the radio galaxies in our sample (~20%) have high, ULIRG-like dust masses, along with evidence for prodigious star formation activity. The latter objects are more likely to have been triggered in major, gas-rich mergers that represent a rapid growth phase for both their host galaxies and their supermassive black holes.Comment: 5 pages, 2 figures, accepted for publication in MNRAS Letter