Fundamental Frequencies in the Schwarzschild Spacetime

We consider the Keplerian, radial and vertical fundamental frequencies in the Schwarzschild spacetime to study the so-called kilohertz quasi-periodic oscillations from low-mass X-ray binary systems. We show that, within the Relativistic Precession Model, the interpretation of observed kilohertz quasi-periodic oscillations in terms of the fundamental frequencies of test particles in the Schwarzschild spacetime, allows one to infer the total mass $M$ of the central object, the internal $R_{in}$ and external $R_{ex}$ radii of accretion disks, and innermost stable circular orbits $r_{ISCO}$ for test particles in a low-mass X-ray binary system. By constructing the relation between the upper and lower frequencies and exploiting the quasi-periodic oscillation data of the Z and Atoll sources we perform the non-linear model fit analysis and estimate the mass of the central object. Knowing the value of the mass we calculate the internal $R_{in}$ and external $R_{ex}$ radii of accretion disks and show that they are larger than $r_{ISCO}$, what was expected.Comment: 7 pages, 6 figures, 1 tabl

Induced gravitational collapse at extreme cosmological distances: the case of GRB 090423

CONTEXT: The induced gravitational collapse (IGC) scenario has been introduced in order to explain the most energetic gamma ray bursts (GRBs), Eiso=10^{52}-10^{54}erg, associated with type Ib/c supernovae (SNe). It has led to the concept of binary-driven hypernovae (BdHNe) originating in a tight binary system composed by a FeCO core on the verge of a SN explosion and a companion neutron star (NS). Their evolution is characterized by a rapid sequence of events: [...]. AIMS: We investigate whether GRB 090423, one of the farthest observed GRB at z=8.2, is a member of the BdHN family. METHODS: We compare and contrast the spectra, the luminosity evolution and the detectability in the observations by Swift of GRB 090423 with the corresponding ones of the best known BdHN case, GRB 090618. RESULTS: Identification of constant slope power-law behavior in the late X-ray emission of GRB 090423 and its overlapping with the corresponding one in GRB 090618, measured in a common rest frame, represents the main result of this article. This result represents a very significant step on the way to using the scaling law properties, proven in Episode 3 of this BdHN family, as a cosmological standard candle. CONCLUSIONS: Having identified GRB 090423 as a member of the BdHN family, we can conclude that SN events, leading to NS formation, can already occur already at z=8.2, namely at 650 Myr after the Big Bang. It is then possible that these BdHNe originate stem from 40-60 M_{\odot} binaries. They are probing the Population II stars after the completion and possible disappearance of Population III stars.Comment: 9 pages, 9 figures, to appear on A&

On the thermal and double episode emissions in GRB 970828

Following the recent theoretical interpretation of GRB 090618 and GRB 101023, we here interpret GRB 970828 in terms of a double episode emission: the first episode, observed in the first 40 s of the emission, is interpreted as the proto-black-hole emission; the second episode, observed after t$_0$+50 s, as a canonical gamma ray burst. The transition between the two episodes marks the black hole formation. The characteristics of the real GRB, in the second episode, are an energy of $E_{tot}^{e^+e^-} = 1.60 \times 10^{53}$ erg, a baryon load of $B = 7 \times 10^{-3}$ and a bulk Lorentz factor at transparency of $\Gamma = 142.5$. The clear analogy with GRB 090618 would require also in GRB 970828 the presence of a possible supernova. We also infer that the GRB exploded in an environment with a large average particle density $\, \approx 10^3$ part/cm$^3$ and dense clouds characterized by typical dimensions of $(4 - 8) \times 10^{14}$ cm and $\delta n/n \propto 10$. Such an environment is in line with the observed large column density absorption, which might have darkened both the supernova emission and the GRB optical afterglow.Comment: 7 pages, 10 figures, submitted to Ap

GRB 081024B and GRB 140402A: two additional short GRBs from binary neutron star mergers

Theoretical and observational evidences have been recently gained for a two-fold classification of short bursts: 1) short gamma-ray flashes (S-GRFs), with isotropic energy $E_{iso}<10^{52}$~erg and no BH formation, and 2) the authentic short gamma-ray bursts (S-GRBs), with isotropic energy $E_{iso}>10^{52}$~erg evidencing a BH formation in the binary neutron star merging process. The signature for the BH formation consists in the on-set of the high energy ($0.1$--$100$~GeV) emission, coeval to the prompt emission, in all S-GRBs. No GeV emission is expected nor observed in the S-GRFs. In this paper we present two additional S-GRBs, GRB 081024B and GRB 140402A, following the already identified S-GRBs, i.e., GRB 090227B, GRB 090510 and GRB 140619B. We also return on the absence of the GeV emission of the S-GRB 090227B, at an angle of $71^{\rm{o}}$ from the \textit{Fermi}-LAT boresight. All the correctly identified S-GRBs correlate to the high energy emission, implying no significant presence of beaming in the GeV emission. The existence of a common power-law behavior in the GeV luminosities, following the BH formation, when measured in the source rest-frame, points to a commonality in the mass and spin of the newly-formed BH in all S-GRBs.Comment: 16 pages, submitted to ApJ, second version addressing the comments by the refere