Study of Faint Galaxies in the Field of GRB 021004

We present an analysis of BVRcIc observations of the field sized around 4' x 4' centered at the host galaxy of the gamma-ray burst GRB 021004 with the 6-m BTA telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences. We measured the magnitudes and constructed the color diagrams for 311 galaxies detected in the field (S/N > 3). The differential and integral counts of galaxies up to the limit, corresponding to 28.5 (B), 28.0 (V), 27.0 (Rc), 26.5 (Ic) were computed. We compiled the galaxy catalog, consisting of 183 objects, for which the photometric redshifts up to the limiting magnitudes 26.0 (B), 25.5 (V), 25.0 (Rc), 24.5 (Ic) were determined using the HyperZ code. We then examined the radial distribution of galaxies based on the z estimates. We have built the curves expected in the case of a uniform distribution of galaxies in space, and obtained the estimates for the size and contrast of the possible super-large-scale structures, which are accessible with the observations of this type.Comment: 15 pages, 7 figures, 2 tables, to be published in Astrophysical Bulletin 65, 311-325 (2010

The earliest spectroscopy of the GRB 030329 afterglow with 6-m telescope

The earliest BTA (SAO RAS 6-m telescope) spectroscopic observations of the GRB 030329 optical transient (OT) are presented, which almost coincide in time with the "first break" ($t\sim 0.5$ day after the GRB) of the OT light curve. The beginning of spectral changes are seen as early as $\sim 10-12$ hours after the GRB. So, the onset of the spectral changes for $t<1$ day indicates that the contribution from Type Ic supernova (SN) into the OT optical flux can be detected earlier. The properties of early spectra of GRB 030329/SN 2003dh can be consistent with a shock moving into a stellar wind formed from the pre-SN. Such a behavior (similar to that near the UV shock breakout in SNe) can be explained by the existence of a dense matter in the immediate surroundings of massive stellar GRB/SN progenitor). The urgency is emphasized of observation of early GRB/SN spectra for solving a question that is essential for understanding GRB physical mechanism: {\it Do all} long-duration gamma-ray bursts are caused by (or physically connected to) {\it ordinary} core-collapse supernovae? If clear association of normal/ordinary core-collapse SNe (SN Ib/c, and others SN types) and GRBs would be revealed in numbers of cases, we may have strong observational limits for gamma-ray beaming and for real energetics of the GRB sources.Comment: 4 pages, 5 figures. Proceedings of the 4th Workshop "Gamma-Ray Bursts in the Afterglow Era", Roma, 2004 October 18-22, eds. L. Piro, L. Amati, S. Covino, and B. Gendre. Il Nuovo Cimento, in pres

On the analysis of data emerging in non-linear and complex systemscomparison of two X-Ray prony spectra

New arguments proving that successive (repeated) measurements have a memory and actually remember each other are presented. The recognition of this peculiarity can change essentially the existing paradigm associated with conventional observation in behavior of different complex systems and lead towards the application of an intermediate model (IM). This IM can provide a very accurate fit of the measured data in terms of the Prony's decomposition. This decomposition, in turn, contains a small set of the fitting parameters relatively to the number of initial data points and allows comparing the measured data in cases where the “best fit” model based on some specific physical principles is absent. As an example, we consider two X-ray diffractometers (defined in paper as A- (“cheap”) and B- (“expensive”) that are used after their proper calibration for the measuring of the same substance (corundum a-Al2O3). The amplitude-frequency response (AFR) obtained in the frame of the Prony's decomposition can be used for comparison of the spectra recorded from (A) and (B) - X-ray diffractometers (XRDs) for calibration and other practical purposes. We prove also that the Fourier decomposition can be adapted to “ideal” experiment without memory while the Prony's decomposition corresponds to real measurement and can be fitted in the frame of the IM in this case. New statistical parameters describing the properties of experimental equipment (irrespective to their internal “filling”) are found. The suggested approach is rather general and can be used for calibration and comparison of different complex dynamical systems in practical purposes

Compton drag as a mechanism for very high linear polarization in Gamma-Ray Bursts

The recent claim by Coburn & Boggs to have detected a very high degree of linear polarization in the prompt emission of GRB 021206 has stimulated interest in how much polarization could arise in gamma-ray bursts from synchrotron emission. Alternatively, as Shaviv & Dar have shown, GRB polarization could be produced by inverse Compton scattering in the point-source limit. We discuss polarization from a fireball that upscatters a soft radiation field. We show that, after the proper angular integration, the residual polarization can be large, in some cases approaching the point-source limit. We discuss the probability of realizing the geometrical conditions in which a large polarization is obtained showing that, for a particularly bright burst as GRB 021206, the detection of polarization at the first attempt in the Compton drag scenario is not unlikely.Comment: Accepted for publication in MNRA

Near-infrared follow-up to the May 2008 activation of SGR 1627-41

On 28 May 2008, the Swift satellite detected the first reactivation of SGR 1627-41 since its discovery in 1998. Following this event we began an observing campaign in near infrared wavelengths to search for a possible counterpart inside the error circle of this SGR, which is expected to show flaring activity simultaneous to the high energy flares or at least some variability as compared to the quiescent state. For the follow-up we used the 0.6m REM robotic telescope at La Silla Observatory, which allowed a fast response within 24 hours and, through director discretionary time, the 8.2m Very Large Telescope at Paranal Observatory. There, we observed with NACO to produce high angular resolution imaging with the aid of adaptive optics. These observations represent the fastest near infrared observations after an activation of this SGR and the deepest and highest spatial resolution observations of the Chandra error circle. 5 sources are detected in the immediate vicinity of the most precise X-ray localisation of this source. For 4 of them we do not detect variability, although the X-ray counterpart experimented a significant decay during our observation period. The 5th source is only detected in one epoch, where we have the best image quality, so no variability constrains can be imposed and remains as the only plausible counterpart. We can impose a limit of Ks > 21.6 magnitudes to any other counterpart candidate one week after the onset of the activity. Our adaptive optics imaging, with a resolution of 0.2" provides a reference frame for subsequent studies of future periods of activity.Comment: Accepted for publication in A&

Study of Envelope Velocity Evolution of Type Ib-c Core-Collapse Supernovae from Observations of XRF 080109 / SN 2008D and GRB 060218 / SN 2006aj with BTA

Results of modeling the spectra of two supernovae SN 2008D and SN 2006aj related to the X-ray flash XRF 080109 and gamma-ray burst GRB / XRF 060218, respectively, are studied. The spectra were obtained with the 6-meter BTA telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences in 6.48 and 27.61 days after the explosion of SN 2008D, and in 2.55 and 3.55 days after the explosion of SN 2006aj. The spectra were interpreted in the Sobolev approximation with the SYNOW code. An assumption about the presence of envelopes around the progenitor stars is confirmed by an agreement between the velocities of lines interpreted as hydrogen and helium, and the empiric power-law velocity drop with time for the envelopes of classic core-collapse supernovae. Detection of a P Cyg profile of the H-beta line in the spectra of optical afterglows of GRBs can be a determinative argument in favor of this hypothesis.Comment: 12 pages, 6 figures, accepted for publication in Astrophysical Bulletin

Taming Nonconvex Stochastic Mirror Descent with General Bregman Divergence

This paper revisits the convergence of Stochastic Mirror Descent (SMD) in the contemporary nonconvex optimization setting. Existing results for batch-free nonconvex SMD restrict the choice of the distance generating function (DGF) to be differentiable with Lipschitz continuous gradients, thereby excluding important setups such as Shannon entropy. In this work, we present a new convergence analysis of nonconvex SMD supporting general DGF, that overcomes the above limitations and relies solely on the standard assumptions. Moreover, our convergence is established with respect to the Bregman Forward-Backward envelope, which is a stronger measure than the commonly used squared norm of gradient mapping. We further extend our results to guarantee high probability convergence under sub-Gaussian noise and global convergence under the generalized Bregman Proximal Polyak-{\L}ojasiewicz condition. Additionally, we illustrate the advantages of our improved SMD theory in various nonconvex machine learning tasks by harnessing nonsmooth DGFs. Notably, in the context of nonconvex differentially private (DP) learning, our theory yields a simple algorithm with a (nearly) dimension-independent utility bound. For the problem of training linear neural networks, we develop provably convergent stochastic algorithms.Comment: Accepted for publication at AISTATS 202