arXiv subjects

V. V. Sokolov

Publications and source records attributed to V. V. Sokolov.

At least 73 records · Page 4Linked to original sources

arXiv2004

Factorization of the current algebra and integrable top-like systems

A hierarchy of integrable hamiltonian nonlinear ODEs is associated with any decomposition of the Lie algebra of Laurent series with coefficients being elements of a semi-simple Lie algebra into a sum of the subalgebra consisting of the Taylor series and some complementary subalgebra. In the case of the Lie algebra $so(3)$ our scheme covers all classical integrable cases in the Kirchhoff problem of the motion of a rigid body in an ideal fluid. Moreover, the construction allows us to generate integrable deformations for known integrable models.

nlin.SI↗

arXiv2004

Earliest spectroscopy of the GRB030329 optical transient

We present the earliest BTA (SAO RAS 6-m telescope) spectroscopic observations of the GRB030329 optical transient (OT), which almost coincide in time with the first "break" (t ~ 0.5 day after the GRB) of the OT light curve. The BTA/MPFS (Multi Pupil Fiber Spectrograph) spectra are clearly not smooth: the OT spectra showed a continuum with several broad spectral features at about 4000, 4450, 5900AA. The OT spectrum showed some evolution starting from the first night after the burst, and the beginning of spectral changes are seen as early as ~10-12 hours after the GRB. 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. So, summarizing our and other spectroscopic data on the OT we confirm the evolution of the OT spectrum and color pointed also by other authors (Hjorth et al. 2003; Matheson et al. 2003b). The early spectra of GRB030329/SN2003dh properties can be consistent with a shock moving into a stellar wind formed from the pre-SN. Such a behavior (similar to one near the UV shock breakout in SNe) can be explained by the existence of a dense matter in the immediate surroundings of GRB/SN progenitor.

astro-ph↗

arXiv2003

Poisson maps and integrable deformations of Kowalevski top

We construct a Poisson map between manifolds with linear Poisson brackets corresponding to the Lie algebras $e(3)$ and $so(4)$. Using this map we establish a connection between the deformed Kowalevski top on $e(3)$ proposed by Sokolov and the Kowalevski top on $so(4)$. The connection between these systems leads to the separation of variables for the deformed system on $e(3)$ and yields the natural $5\times 5$ Lax pair for the Kowalevski top on $so(4)$.

nlin.SI↗

arXiv2003

Is the concept of the non-Hermitian effective Hamiltonian relevant in the case of potential scattering?

We examine the notion and properties of the non-Hermitian effective Hamiltonian of an unstable system using as an example potential resonance scattering with a fixed angular momentum. We present a consistent self-adjoint formulation of the problem of scattering on a finite-range potential, which is based on separation of the configuration space on two, internal and external, segments. The scattering amplitude is expressed in terms of the resolvent of a non-Hermitian operator H. The explicit form of this operator depends both on the radius of separation and the boundary conditions at this place which can be chosen in many different ways. We discuss this freedom and show explicitly that the physical scattering amplitude is, nevertheless, unique though not all choices are equally adequate from the physical point of view. The energy-dependent operator H should not be confused with the non-Hermitian effective Hamiltonian H_{eff} exploited usually to describe interference of overlapping resonances. We apply the developed formalism to a chain of L delta-barriers whose solution is also found independently in a closed form. For a fixed band of L overlapping resonances, the smooth energy dependence of H can be ignored so that complex eigenvalues of the LxL submatrix H_{eff} define the energies and widths of the resonances.We construct H_{eff} for the two commonly considered types of the boundary conditions (Neumann and Dirichlet) for the internal motion. Formation in the outer well of a short-lived doorway state is explicitly demonstrated together with the appearance of L-1 long-lived states trapped in the inner part of the chain.

cond-mat.mes-hall↗

arXiv2002

Subaru optical observations of the old pulsar PSR B0950+08

We report the B band optical observations of an old (17.5 Myr) radiopulsar PSR B0950+08 obtained with the Suprime-Cam at the Subaru telescope. We detected a faint object, B=27.07(16). Within our astrometrical accuracy it coincides with the radio position of the pulsar and with the object detected earlier by Pavlov et al. (1996) in UV with the HST/FOC/F130LP. The positional coincidence and spectral properties of the object suggest that it is the optical counterpart of PSR B0950+08. Its flux in the B band is two times higher than one would expect from the suggested earlier Rayleigh-Jeans interpretation of the only available HST observations in the adjacent F130LP band. Based on the B and F130LP photometry of the suggested counterpart and on the available X-ray data we argue in favour of nonthermal origin of the broad-band optical spectrum of PSR B0950+08, as it is observed for the optical emission of the younger, middle-aged pulsars PSR B0656+14 and Geminga. At the same time, the optical efficiency of PSR B0950+08, estimated from its spin-down power and the detected optical flux, is by several orders of magnitude higher than for these pulsars, and comparable with that for the much younger and more energetic Crab pulsar. We cannot exclude the presence of a compact, about 1'', faint pulsar nebula around PSR B0950+08, elongated perpendicular to the vector of its proper motion, unless it is not a projection of a faint extended object on the pulsar position.

astro-ph↗

arXiv2001

Commutative Poisson subalgebras for the Sklyanin bracket and deformations of known integrable models

A hierarchy of commutative Poisson subalgebras for the Sklyanin bracket is proposed. Each of the subalgebras provides a complete set of integrals in involution with respect to the Sklyanin bracket. Using different representations of the bracket, we find some integrable models and a separation of variables for them. The models obtained are deformations of known integrable systems like the Goryachev-Chaplygin top, the Toda lattice and the Heisenberg model.

nlin.SI↗

arXiv2001

On the GRB progenitors: possible consequences for supernovae connection with gamma-ray bursts

Unique data on $BVRI$ light curves of the optical transient (OT) of GRB 970508 obtained with the 6-m telescope have been interpreted in the framework of the idea of a straightforward link between supernovae (SNe) and long duration gamma-ray bursts (GRBs). The effect must be maximum in the $I_{c}$ band as for OT GRB 970228. The peak absolute ($M_{B}$) magnitude of the suggested SN must be around -19.5 for the OT of GRB 970508. So, in addition to the characteristic "shoulders" on the light curves of the OTs of GRB 970228, GRB 980326, 990712, 991208, more evidence of the link between GRBs and Type Ib/c SNe (or core-collapse SNe) was found, which could be an argument in favor of the idea of massive stars as progenitors of long duration GRBs. If all or the main part of long duration GRBs are associated with the SNe, GRB host galaxies (for ground-based observations, at least) must be dimmer than the peak magnitude of a SN. If some GRB/SN relation really exists, and if all or at least the main part of long duration GRBs are associated with SNe, then as a consequence we have a very strong $γ$-ray beaming with a solid angle of up to $Ω_{beam} \sim (10^{-5} - 10^{-6})\cdot 4π$. Besides, the observations of K$_α$ lines of iron in the X-ray afterglow spectra of GRBs (970508, 970828, 991216, 000214) and the observation of redshifted absorption feature of neutral iron (7.1 keV) simultaneously with GRB 990705 are also evidence in favor of massive stars -- progenitors of GRBs.

astro-ph↗

arXiv2001

Host Galaxies of Gamma-ray Bursts: Spectral Energy Distributions and Internal Extinction

We present BVRcIc broad-band flux spectra for the host galaxies of GRB970508, GRB980613, GRB980703, GRB990123 and GRB991208 obtained with the 6-m telescope of SAO RAS. The BVRcIc of these hosts are best fitted by the spectral properties of template SEDs of starburst galaxies and that there is a significant internal extinction in these host galaxies. We derived the absolute magnitudes of the GRB host galaxies making use of SEDs for the starburst galaxies. We performed the population synthesis modeling of the continuum spectral energy distribution of the host galaxies of GRB970508 and GRB980703 using different extinction laws and assuming burst and exponential scenarios of star formation. The comparison of BVRcIc broad-band flux spectra with the local starburst galaxies templates and theoretical templates as well as direct estimates (using Balmer emission lines) of the internal extinction shows that it is likely to be of great importance to take into account effects of the internal extinction in the host galaxies. From the SED of the host galaxy of GRB991208 and from the intensity of their spectral lines it follows that this is a GRB galaxy with the highest massive star-formation rate of all known GRB galaxies. The reduced luminosity of these dusty galaxies (e.g. for the host of GRB970508 A_V\sim 2 mag, for the host of GRB980703 A_V\sim 0.6 mag and for the host of GRB991208 A_V\sim 2 mag) could explain the observational fact: none of the observed GRB host galaxies with known distances is brighter than the local galaxies with the luminosity L_*.

astro-ph↗

arXiv2001

Evidence for a Supernova in the Ic Band Light Curve of the Optical Transient of GRB 970508

Unique data on $BVRI$ brightness curves of the OT of GRB 970508 obtained with the 6-m telescope have been interpreted in the framework of the GRB-SN (supernovae) connection. The effect must be maximal in the I_c band as OT GRB 970228. The peak absolute (M_B) magnitude of the suggested SN must be around -19.5 for the OT of GRB 970508. If all or the main part of long GRBs are associated with SNe, the GRB host galaxies (for ground-based observations, at least) must be dimmer than the peak magnitude of the SN.

astro-ph↗

arXiv2001

The Multiband Photometry of GRB Host Galaxies: Comparison with the Spectral Energy Distributions of Nearby and Theoretical Modeling Galaxies

We present one of the results of $BVRI$ photometry of the hosts of GRB for the host galaxy of GRB 970508 and the theoretical modeling of its continuum spectral energy distribution (SED) to show that it is important to take into account internal extinction in the host galaxies. We compared the BVRI broad-band flux spectrum of the host to template SEDs of local starburst galaxies and found that there is a significant internal extintion in this host. Moreover, this comparison allows us to derive the absolute magnitude (M_{B_{rest}}) and rouhgly estimate reddening (A_V). Population synthesis modeling of the continuum SED for different reddening laws demostrates that the observational data of the host galaxy of GRB 970508 are best fitted by the spectral properties of a model SED with extinction of A_V\approx 2.

astro-ph↗

arXiv2001

The extraordinarily bright optical afterglow of GRB 991208 and its host galaxy

Observations of the extraordinarily bright optical afterglow (OA) of GRB 991208 started 2.1 d after the event. The flux decay constant of the OA in the R-band is -2.30 +/- 0.07 up to 5 d, which is very likely due to the jet effect, and after that it is followed by a much steeper decay with constant -3.2 +/- 0.2, the fastest one ever seen in a GRB OA. A negative detection in several all-sky films taken simultaneously to the event implies either a previous additional break prior to 2 d after the occurrence of the GRB (as expected from the jet effect). The existence of a second break might indicate a steepening in the electron spectrum or the superposition of two events. Once the afterglow emission vanished, contribution of a bright underlying SN is found, but the light curve is not sufficiently well sampled to rule out a dust echo explanation. Our determination of z = 0.706 indicates that GRB 991208 is at 3.7 Gpc, implying an isotropic energy release of 1.15 x 10E53 erg which may be relaxed by beaming by a factor > 100. Precise astrometry indicates that the GRB coincides within 0.2" with the host galaxy, thus given support to a massive star origin. The absolute magnitude is M_B = -18.2, well below the knee of the galaxy luminosity function and we derive a star-forming rate of 11.5 +/- 7.1 Mo/yr. The quasi-simultaneous broad-band photometric spectral energy distribution of the afterglow is determined 3.5 day after the burst (Dec 12.0) implying a cooling frequency below the optical band, i.e. supporting a jet model with p = -2.30 as the index of the power-law electron distribution.

astro-ph↗

arXiv2000

Observation of X-ray lines from a Gamma-Ray Burst (GRB991216): Evidence of Moving Ejecta from the Progenitor

We report on the discovery of two emission features observed in the X-ray spectrum of the afterglow of the gamma-ray burst (GRB) of 16 Dec. 1999 by the Chandra X-Ray Observatory. These features are identified with the Ly$_α$ line and the narrow recombination continuum by hydrogenic ions of iron at a redshift $z=1.00\pm0.02$, providing an unambiguous measurement of the distance of a GRB. Line width and intensity imply that the progenitor of the GRB was a massive star system that ejected, before the GRB event, $\approx 0.01 \Ms$ of iron at a velocity $\approx 0.1 c$, probably by a supernova explosion.

astro-ph↗

arXiv2000

Optical photometry of the PSR B0656+14 and its neighborhood

We present the results of the broad-band photometry of the nearby middle-aged radio pulsar PSR B0656+14 and its neighborhood obtained with the 6-meter telescope of the SAO RAS and with the Hubble Space Telescope. The broad-band spectral flux $F_ν$ of the pulsar decreases with increasing frequency in the near-IR range and increases with frequency in the near-UV range. The increase towards UV can be naturally interpreted as the Rayleigh-Jeans tail of the soft thermal component of the X-ray spectrum emitted from the surface of the cooling neutron star. Continuation of the power-law component, which dominates in the high-energy tail of the X-ray spectrum, to the IR-optical-UV frequencies is consistent with the observed fluxes. This suggests that the non-thermal pulsar radiation may be of the same origin in a broad frequency range from IR to hard X-rays. We also studied 4 objects detected in the pulsar's 5" neighborhood.

astro-ph↗

arXiv2000

The Multiband Photometry of the GRB Host Galaxies

We present photometric multiband spectral energy distributions for the GRB host galaxies: GRB 971214, GRB 970508, GRB 980613, GRB 980703 and GRB 990123 obtained with the 6-m telescope of SAO RAS. Using SEDs for the starburst galaxies, we made estimates of K-correction values and estimated the absolute magnitudes of the GRB host galaxies within the range of cosmological parameters. The comparison of the broad band spectra of these galaxies with the spectra of galaxies of different morphological types (Connolly et al, 1995, AJ, 110, 1071) shows that the GRB host galaxies are best fitted by the spectral properties of S2-S5 averaged SEDs of starburst galaxies.

astro-ph↗

arXiv2000

Photometric study of fields of nearby pulsars with the 6m telescope

Fields of Geminga, PSR B0950+08, PSR J1908+0734 and PSR J0108-1431 have been observed within the program of optical investigation of nearby neutron stars carried out with the 6m telescope. Our multicolour BVR_cI_c photometry has yielded the following magnitudes of Geminga: V=25.3+/-0.4; R_c=25.4+/-0.3. The estimates of the 3σupper limits in the B and I_c bands are 25.4 and 24.9, respectively. This is in agreement with previous observations of Geminga. We have suggested candidate for optical counterpart of PSR B0950+08, with R_c=25.4+/-0.3. When compared to the HST data obtained in UV its flux shows that this old pulsar can be brighter in near-IR than in near-UV. We have obtained for the first time images of the fields of PSR J1908+0734 and PSR J0108-1431. Although no optical counterparts have been detected, the magnutude upper limits obtained suggest further observations of these pulsars.

astro-ph↗

arXiv2000

BVRcIc photometry of GRB 980703 and GRB 990123 host galaxies

We present a photometry of GRB 980703 and GRB 990123 host galaxies which was performed about 20 days and a half year after gamma-ray bursts occured, respectively. The contributions of the optical transiets (OT) were negligible in both cases. We derived broad band BVR_cI_c spectra of the host galaxies and compared them to continuum spectra of different Hubble-type galaxies and averaged spectra of starburst galaxies. For H_0=60 km s^{-1} Mpc^{-1} and three Friedmann cosmological models with matter density and cosmological constant parameters (Omega_m,Omega_Lambda) = (1,0),(0,0),(0,1) we estimated M_Brest and star-forming rates (SFRs) using the fluxes in photometric bands for the host galaxies. Within the range of cosmological parameters our estimates of the absolute magnitudes are: M_Brest = -20.60 .. -21.73 for the GRB 980703 host galaxy and M_Brest = -20.20 .. -21.82 for the GRB 990123 host galaxy. We obtained estimates of K-correction values and absolute magnitudes of the host galaxies using SEDs for star-forming galaxies.

astro-ph↗

arXiv1999

Quantum Resonances and Regularity Islands in Quantum Maps

We study analytically as well as numerically the dynamics of a quantum map near a quantum resonance of an order q. The map is embedded into a continuous unitary transformation generated by a time-independent quasi-Hamiltonian. Such a Hamiltonian generates at the very point of the resonance a local gauge transformation described the unitary unimodular group SU(q). The resonant energy growth of is attributed to the zero Liouville eigenmodes of the generator in the adjoint representation of the group while the non-zero modes yield saturating with time contribution. In a vicinity of a given resonance, the quasi-Hamiltonian is then found in the form of power expansion with respect to the detuning from the resonance. The problem is related in this way to the motion along a circle in a (q^2-1)-component inhomogeneous "magnetic" field of a quantum particle with $q$ intrinsic degrees of freedom described by the SU(q) group. This motion is in parallel with the classical phase oscillations near a non-linear resonance. The most important role is played by the resonances with the orders much smaller than the typical localization length, q << l. Such resonances master for exponentially long though finite times the motion in some domains around them. Explicit analytical solution is possible for a few lowest and strongest resonances.

chao-dyn↗

arXiv1999

Integrable ODEs on Associative Algebras

In this paper we give definitions of basic concepts such as symmetries, first integrals, Hamiltonian and recursion operators suitable for ordinary differential equations on associative algebras, and in particular for matrix differential equations. We choose existence of hierarchies of first integrals and/or symmetries as a criterion for integrability and justify it by examples. Using our componentless approach we have solved a number of classification problems for integrable equations on free associative algebras. Also, in the simplest case, we have listed all possible Hamiltonian operators of low order.

solv-int↗