Abstract. We note that the recently discovered 450 Hz frequency in the X-ray flux of the black hole candidate GRO J1655-40 is in a 3:2 ratio to the previously known 300 Hz frequency of quasi-periodic oscillations (QPO) in the same source. If the origin of high frequency QPOs in black hole systems is a resonance between orbital and epicyclic motion of accreting matter, as suggested previously, the angular momentum of the black hole can be accurately determined, given its mass. We find that the dimensionless angular momentum is in the range 0.2 < j < 0.67 if the mass is in the (corresponding) range of 5.5 to 7.9 solar masses. Key words. equation of state -relativity -stars: black holes -X-raysWe have previously suggested that "twin" kHz QPOs in accreting neutron stars arise as a result of non-linear 1:2 or 1:3 resonance between the radial epicyclic motion and the orbital motion of matter in a nearly Keplerian accretion disk. As a corollary, we have noted (Kluźniak & Abramowicz 2001) that the same phenomenon should also arise in accreting black holes, where only a single high frequency had been observed. Strohmayer (2001) now reports the discovery of a second QPO in GRO J1655-40, a well known black hole candidate in a low-mass X-ray binary, with the mass of the compact X-ray source determined from optical studies to be in the range 5.9 < M/M < 7.9 (Shabhaz et al. 1999). There are time intervals, when both QPOs are present at the same time.The two QPOs now known in the source occur at frequencies 300 Hz and 450 Hz, i.e., in a 2:3 ratio, strongly supporting the notion of a resonance in the system. (The effects of orbital resonances are commonly observed in the solar system -the rotation of the Moon and gaps in the rings of Saturn are well known examples.) Of all rational ratios only 2:3, 1:2 and 1:3 resonances are capable of giving a 2:3 ratio of frequencies. Specifically, if the lower frequency in the resonance is ω, and the higher frequency Ω, the only possibilities are that Ω = 300 Hz and Ω + ω = 450 Hz for the 1:2 resonance, or that Ω = 450 Hz and Ω − ω = 300 Hz for the 1:3 resonance.Send offprint requests to: W. Kluźniak, e-mail: wlodek@camk.edu.plIn the spirit of Kluźniak & Abramowicz (2001), we consider resonances between orbital and epicyclic motion in the Kerr metric. The fluid in a geometrically thin and axially symmetric accretion disk follows circular orbits, and any departures (caused by gradients of pressure) from circular geodesic motion are second order in the small parameter of characteristic thickness divided by the radius of the disk. We assume that an n:m resonance can be excited at or near that radius where the ratio of the epicyclic frequency to the orbital frequency is n:m. The formulae for the frequencies can be found, e.g., in the review by Kato (2001) and references therein. We find, for instance, that for j = 0.2 (see below) the radial epicyclic frequency is in a 1:2 resonance with orbital frequency at r = 7.22 M , i.e., at 3.6 Schwarzschild radii. For j = 0.67, the same frequencies are in ...

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Gamma-ray line signatures can be expected in the very-high-energy (E(γ)>100 GeV) domain due to self-annihilation or decay of dark matter (DM) particles in space. Such a signal would be readily distinguishable from astrophysical γ-ray sources that in most cases produce continuous spectra that span over several orders of magnitude in energy. Using data collected with the H.E.S.S. γ-ray instrument, upper limits on linelike emission are obtained in the energy range between ∼ 500 GeV and ∼ 25 TeV for the central part of the Milky Way halo and for extragalactic observations, complementing recent limits obtained with the Fermi-LAT instrument at lower energies. No statistically significant signal could be found. For monochromatic γ-ray line emission, flux limits of (2 × 10(-7) -2 × 10(-5)) m(-2) s(-1) sr(-1) and (1 × 10(-8) -2 × 10(-6)) m(-2) s(-1)sr(-1) are obtained for the central part of the Milky Way halo and extragalactic observations, respectively. For a DM particle mass of 1 TeV, limits on the velocity-averaged DM annihilation cross section ⟨σv⟩(χχ → γγ) reach ∼ 10(-27) cm(3)s(-1), based on the Einasto parametrization of the Galactic DM halo density profile.

A search for a very-high-energy (VHE; ≥100  GeV) γ-ray signal from self-annihilating particle dark matter (DM) is performed towards a region of projected distance r∼45-150  pc from the Galactic center. The background-subtracted γ-ray spectrum measured with the High Energy Stereoscopic System (H.E.S.S.) γ-ray instrument in the energy range between 300 GeV and 30 TeV shows no hint of a residual γ-ray flux. Assuming conventional Navarro-Frenk-White and Einasto density profiles, limits are derived on the velocity-weighted annihilation cross section (σv) as a function of the DM particle mass. These are among the best reported so far for this energy range and in particular differ only little between the chosen density profile parametrizations. In particular, for the DM particle mass of ∼1  TeV, values for (σv) above 3×10(-25)  cm(3) s(-1) are excluded for the Einasto density profile.