Massive vector fields on the Schwarzschild spacetime: quasinormal modes and bound states

We study the propagation of a massive vector or Proca field on the Schwarzschild spacetime. The field equations are reduced to a one-dimensional wave equation for the odd-parity part of the field and two coupled equations for the even-parity part of the field. We use numerical techniques based on solving (scalar or matrix-valued) three-term recurrence relations to compute the spectra of both quasi-normal modes and quasi-bound states, which have no massless analogue, complemented in the latter case by a forward-integration method. We study the radial equations analytically in both the near-horizon and far-field regions and use a matching procedure to compute the associated spectra in the small-mass limit. Finally, we comment on extending our results to the Kerr geometry and its phenomenological relevance for hidden photons arising e.g. in string theory compactifications.Comment: 15 pages, 8 figures; minor corrections, to be published in Phys. Rev.

Scaling and correlations in the dynamics of forest-fire occurrence

Forest-fire waiting times, defined as the time between successive events above a certain size in a given region, are calculated for Italy. The probability densities of the waiting times are found to verify a scaling law, despite that fact that the distribution of fire sizes is not a power law. The meaning of such behavior in terms of the possible self-similarity of the process in a nonstationary system is discussed. We find that the scaling law arises as a consequence of the stationarity of fire sizes and the existence of a non-trivial ``instantaneous'' scaling law, sustained by the correlations of the process.Comment: Not a long paper, but many figures (but no large size in kb

Galactic Extinction from Colors and Counts of Field Galaxies in WFPC2 Frames: An Application to GRB 970228

We develop the ``simulated extinction method'' to measure average foreground Galactic extinction from field galaxy number-counts and colors. The method comprises simulating extinction in suitable reference fields by changing the isophotal detection limit. This procedure takes into account selection effects, in particular, the change in isophotal detection limit (and hence in isophotal magnitude completeness limit) with extinction, and the galaxy color--magnitude relation. We present a first application of the method to the HST WFPC2 images of the gamma-ray burster GRB 970228. Four different WFPC2 high-latitude fields, including the HDF, are used as reference to measure the average extinction towards the GRB in the F606W passband. From the counts, we derive an average extinction of A_V = 0.5 mag, but the dispersion of 0.4 mag between the estimates from the different reference fields is significantly larger than can be accounted by Poisson plus clustering uncertainties. Although the counts differ, the average colors of the field galaxies agree well. The extinction implied by the average color difference between the GRB field and the reference galaxies is A_V = 0.6 mag, with a dispersion in the estimated extinction from the four reference fields of only 0.1 mag. All our estimates are in good agreement with the value of 0.81\pm0.27 mag obtained by Burstein & Heiles, and with the extinction of 0.78\pm0.12 measured by Schlegel et al. from maps of dust IR emission. However, the discrepancy between the widely varying counts and the very stable colors in these high-latitude fields is worth investigating.Comment: 14 pages, 2 figures; submitted to the Astrophysical Journa

Star formation in the giant HII regions of M101

The molecular components of three giant HII regions (NGC 5461, NGC 5462, NGC 5471) in the galaxy M101 are investigated with new observations from the James Clerk Maxwell Telescope, the NRAO 12-meter, and the Owens Valley millimeter array. Of the three HII regions, only NGC 5461 had previously been detected in CO emission. We calculate preliminary values for the molecular mass of the GMCs in NGC 5461 by assuming a CO-to-H_2 factor (X factor) and then compare these values with the virial masses. We conclude that the data in this paper demonstrate for the first time that the value of X may decrease in regions with intense star formation. The molecular mass for the association of clouds in NGC 5461 is approximately 3x10^7 Mo and is accompanied by 1-2 times as much atomic mass. The observed CO emission in NGC 5461 is an order of magnitude stronger than in NGC 5462, while it was not possible to detect molecular gas toward NGC 5471 with the JCMT. An even larger ratio of atomic to molecular gas in NGC 5471 was observed, which might be attributed to efficient conversion of molecular to atomic gas. The masses of the individual clouds in NGC 5461, which are gravitationally bound, cover a range of (2-8) x 10^5 Mo, comparable with the masses of Galactic giant molecular clouds (GMCs). Higher star forming efficiencies, and not massive clouds, appear to be the prerequisite for the formation of the large number of stars whose radiation is required to produce the giant HII regions in M101.Comment: 32 pages, 5 figures, accepted for publication in the Astrophysical Journa