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Topology, which originated as a mathematical discipline, nowadays advances the understanding of many branches of science and technology from elementary particle physics and cosmology to condensed matter physics. In optics, the topology of light and darkness facilitates new degrees of freedom for sculpting optical beams beyond conventionally used amplitude, phase, and polarization. This fundamentally new, spatial dimension opens new opportunities for several optical applications, ranging from optical manipulation, trapping, data processing, optical sensing and metrology, enhanced imaging, and microscopy, to classical and quantum communications. While topological stability of mathematical knots implying robustness to perturbations suggests their potential as information carriers, the behavior of optical knots in perturbative environments such as atmospheric turbulence is largely unexplored. Here, we experimentally and theoretically investigate the effects of atmospheric turbulence of optical knot stability and demonstrate that the number of crossing (the topological invariant) is preserved in the weak-turbulence regime, but may not be conserved in the stronger turbulence conditions. The turbulent medium is simulated in the laboratory using phase screens, which carry the refractive index changes associated with the Kolmogorov power spectrum, encoded in a spatial light modulator. The optical knots are reconstructed by single-shot measurements of the complex field, and the resilience of the knot topology is analyzed for various realistic turbulence strengths. These studies may give rise to entirely new approaches to the three-dimensional (3D) spatially resolved probing of turbulence., Comment: 23 pages and 11 figures

We present the results of a new stage of the long-term photometric study of FG Sge which is a quickly evolving central star of the planetary nebula Hen 1-5. Our new observations carried out on the SAI MSU telescopes in the optical ($BVR_CI_C$) and infrared (IR) ($JHKLM$) regions in 2008-2021 and 2013-2021, respectively, allowed us to trace the evolution of the star's brightness in recent years. The most significant observations were performed in 2019 when the star suffered a short clearing of the dust shell and became visible in $BVR_C$. Based on the spectral energy distribution of FG Sge in the 0.4-5 $\mu$m wavelength range we derived the dust shell parameters: the size of dust grains $a=0.01\mu$m, the inner radius temperature $T_{\text{dust}}=900$ K, optical depth $\tau (K)=0.5$ ($\tau (V)=4.5$), the total mass of dust $M_{\text{dust}}=7\cdot10^{-5} M_{\odot}$. After the short-term clearing of the dust shell in 2019, another dust structure was ejected that resulted in the star fading in all the observed bands. Based on the IR brightness and color curves, we estimated the dust depth growth in 2019-2020., Comment: 17 pages, 9 figures, 3 tables. Accepted for publication in Astronomy Letters

CCD BVRI photometry is presented for the type Ic-BL Supernovae 2016coi and 2018ebt. The shape of the light curves for both objects is typical for this class of SNe. A change of brightness decline rate at about 100 days after maximum light is observed for SN 2016coi. The light curves of SN 2018ebt are best matched by those of SN Ic-BL 2002ap. For SN 2018ebt, we derived the dates and magnitudes of maximum light, rates of decline at late stages of evolution and presented evidence for extinction in the host galaxy being negligible., Comment: 10 pages, 5 figures

We present optical photometric observations of SN 2018aoq from 2 to 100 days after explosion, and 7 spectra at epochs from 11 to 71 days. The light curves and spectra are typical for SNe II-P. As previously reported, SN 2018aoq appears to be of intermediate brightness between subluminous and normal SNe II-P. SN 2018aoq was discovered in Seyfert galaxy NGC 4151, for which the distance is uncertain. We utilised the Expanding Photosphere Method using three sets of filter combinations and velocities derived from the absorption minima of FeII lines and obtained a distance of 20.0 +-1.6 Mpc. The Standard Candle Method applied to SN 2018aoq yields a distance of 16.6 +-1.1 Mpc. Both values are consistent with the distance measurements for NGC 4151 based on geometric method., Comment: 7 pages, 3 figures, submitted to MNRAS

It is shown that inhomogeneous broadening of the spectral line of active impurities may sustain simultaneously parity (P) and time (T) symmetries of a medium, in a finite range of field frequencies, what is forbidden by the causality principle in media without broadening. If a spectral width of a propagating pulse is less than the inhomogeneous broadening, the medium for such a pulse becomes quasi-PT symmetric. The effect of the broadband quasi-PT symmetry in a finite frequency domain, is illustrated on examples of unidirectional diffraction of pulses in Bragg and Laue geometries, propagating in photonic crystals., Comment: Phys. Rev. A (accepted); https://journals.aps.org/pra/accepted/ce070Y82C351455dd5b757a1abc23d0175d9d93a9; 9 pages, 5 figures

We present UBVRI photometry of the supernova 2017eaw in NGC 6946, obtained in the period from May 14 until December 7, 2017. We derive dates and magnitudes of maximum light in the UBVRI bands and the parameters of the light curves. We discuss colour evolution, extinction and maximum luminosity of SN 2017eaw. Preliminary modeling is carried out, and the results are in satisfactory agreement with the light curves in the UBVRI bands., Comment: 15 pages, 6 figures, accepted by Astronomy Letters

We present medium-resolution spectroscopy and multicolor photometry for the optical transient PSN J09093496+3307204 (SN 2015bh) in the galaxy NGC 2770, which has transferred into the supernova phase. The observations were carried out between February 2015 to May 2016. Both at the phase of the SN impostor (2015a) and at the supernova phase (2015b), besides Balmer emissions, the strong Fe II emissions are seen in the spectrum; so, these spectra resemble those of Williams Fe II type classical novae. The star is located near the edge of a dark nebula and notably absorbed (Av = 1.14 +/-0.15 mag). Taking into account this absorption, we determined maximum absolute magnitudes of Mv = -15.0 +/-0.3 mag at the 2015a phase and of Mv = -18.14 +/-0.30 mag at the 2015b phase. The light curve at the 2015b phase is similar to those of SN IIL. The supernova progenitor is a luminous blue variable (LBV) star with the powerful H{\alpha} emission. We considered several hypotheses of supernovae explosions following optical transients related with LBV. The hypothesis of core collapse of an evolved massive star interrupting the process of its merging with massive companion in a binary system (a failed luminous red nova) was chosen as the preferable one for this event., Comment: 28 pages, 8 figures, 2 tables, submitted to Astrophysical Bulletin

We present CCD BVRI photometry for PSN J07285387+3349106 in NGC 2388 collected from 2015 February 17 until March 17. Decaying by 3.6 mag in the R band in the first 20 days post-maximum, this object is among the fastest supernovae observed to date. The peak absolute R magnitude exceeds -18.7 and may be as high as -20.1., Comment: 4 pages, 2 figures in IBVS No. 6140, 2015

We present ultraviolet, optical and near-infrared data of the Type Ibn supernovae (SNe) 2010al and 2011hw. SN 2010al reaches an absolute magnitude at peak of M(R) = -18.86 +- 0.21. Its early light curve shows similarities with normal SNe Ib, with a rise to maximum slower than most SNe Ibn. The spectra are dominated by a blue continuum at early stages, with narrow P-Cygni He I lines indicating the presence of a slow-moving, He-rich circumstellar medium. At later epochs the spectra well match those of the prototypical SN Ibn 2006jc, although the broader lines suggest that a significant amount of He was still present in the stellar envelope at the time of the explosion. SN 2011hw is somewhat different. It was discovered after the first maximum, but the light curve shows a double-peak. The absolute magnitude at discovery is similar to that of the second peak (M(R) = -18.59 +- 0.25), and slightly fainter than the average of SNe Ibn. Though the spectra of SN 2011hw are similar to those of SN 2006jc, coronal lines and narrow Balmer lines are cleary detected. This indicates substantial interaction of the SN ejecta with He-rich, but not H-free, circumstellar material. The spectra of SN 2011hw suggest that it is a transitional SN Ibn/IIn event similar to SN 2005la. While for SN 2010al the spectro-photometric evolution favours a H-deprived Wolf-Rayet progenitor (of WN-type), we agree with the conclusion of Smith et al. (2012) that the precursor of SN 2011hw was likely in transition from a luminous blue variable to an early Wolf-Rayet (Ofpe/WN9) stage., Comment: 23 pages, 11 figures, 6 tables. Accepted by MNRAS

We present UBVRI photometry of the supernova 2014J in M82, obtained in the period from January 24 until March 3, 2014, as well as two spectra, taken on February 4 and March 5. We derive dates and magnitudes of maximum light in the UBVRI bands, the light curve parameters Delta m(15) and expansion velocities of the prominent absorption lines. We discuss colour evolution, extinction and maximum luminosity of SN 2014J., Comment: 10 pages, 4 figures, submitted to Contrib. Astron. Obs. Skalnate Pleso

We present UBVRI photometry of the supernova 2011fe in M101, obtained in the interval of 1-652 days after its discovery, as well as one spectrum, taken 105 days after the brightness maximum in the B band. We derived parameters of the light curves, constructed the colour curves and a "quasi-bolometric" light curve. The light curves, colour evolution and spectrum of the object indicate that SN 2011fe belongs to the "normal" subset of type Ia supernovae. It is practically identical to a well-studied "normal" SN Ia 2003du., Comment: 16 pages, 6 figures

The interstellar medium in the region of a family of cometary globules including the reflection nebula GM 2-39 has been analyzed basing on our observations with the slit spectrograph, the results of our previous observations with a Fabry-Perot interferometer in the H-alpha line, Spitzer archival data together with CO microwave data. The structure of globules' IR emission, velocity field of ionized gas in the H-alpha line and of molecular gas in the CO line have been considered. We have detected a CO cavern around the eastern globules and faint high-velocity H-alpha features of surrounding gas. The most probable sources of ionizing radiation and wind of the Cyg OB1 association responsible for the globules' formation are proposed. Based on our multicolour photometry, it has been found that the brightest compact source in the southern 'head' of the cometary globule - the star HBHA 3703-01 (IRAS 20153+3850) - is a B(5-6)V star with E(B-V)=1.18 mag. The strong and broad H-alpha emission line was revealed in its spectrum. The spectral energy distribution of HBHA 3703-01 in the 0.44-24 micron range has been modeled. It is shown that the star has a hot dust envelope with T(dust)=1400 K and tau(V)=1.1. Besides, the star HBHA 3703-01 illuminates the encompassing diffuse nebula GM 2-39 with a diameter of about 30 arcsec. With regard to all obtained observational data for HBHA 3703-01, this object may be classified as the Herbig Ae/Be star., Comment: Accepted by MNRAS. 12 pages, 8 figures (Fig 1 and 6 are color), 3 tables

CCD UBVRI photometry is presented for type IIb SN 2011dh for about 300 days. The main photometric parameters are derived and the comparison with SNe of similar types is reported. The light curves are similar to those for SN IIb 2008ax, but the initial flash is stronger and very short, and there are humps on the light curves in U and B at the onset of linear decline. Preliminary modeling is carried out, and the results are compared to the quasi-bolometric light curve and to the light curves in UBVRI bands., Comment: 14 pages, 9 figures, submitted to Variable Stars (Peremennye Zvezdy)

We present the results of our UBVRI CCD photometry for the second brightest supernova of 2009, SN 2009nr, discovered during a sky survey with the telescopes of the MASTER robotic network. Its light and color curves and bolometric light curves have been constructed. The light-curve parameters and the maximum luminosity have been determined. SN 2009nr is shown to be similar in light-curve shape and maximum luminosity to SN 1991T, which is the prototype of the class of supernovae Ia with an enhanced luminosity. SN 2009nr exploded far from the center of the spiral galaxy UGC 8255 and most likely belongs to its old halo population. We hypothesize that this explosion is a consequence of the merger of white dwarfs.

We present photometry and spectroscopy of the type IIP supernova 2009bw in UGC 2890 from few days after the outburst to 241 days. The light curve of SN 2009bw during the photospheric phase is similar to that of normal SNe IIP but with brighter peak and plateau (Mmax R = -17.82 mag, Mplateau R = -17.37 mag). The luminosity drop from the photospheric to the nebular phase is one of the fastest ever observed, ~2.2 mag in about 13 days. The radioactive tail of the bolometric light curve indicates that the amount of ejected 56 Ni is \approx 0.022 M\odot. The photospheric spectra reveal high velocity lines of H{\alpha} and H{\beta} until about 105 days after the shock breakout, suggesting a possible early interaction between the SN ejecta and pre-existent circumstellar material, and the presence of CNO elements. By modeling the bolometric light curve, ejecta expansion velocity and photospheric temperature, we estimate a total ejected mass of 8-12M\odot, a kinetic energy of ~0.3 foe and an initial radius of ~ 3.6 - 7 \times 10^13 cm., Comment: Accepted for publication in MNRAS, 19 pages, 13 figures, 9 tables

This paper describes the aims, objectives and first results of the observational program for the study of distant core-collapse supernovae (SNe) with redshifts z < 0.3. This work is done within the framework of an international cooperation program on the SNe monitoring at the 6-m BTA telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences, and other telescopes. We study both the early phases of events (SN type determination, redshift estimation, and a search for manifestations of a wind envelope), and the nebular phase (the effects of explosion asymmetry). The SNe, associated with cosmic gamma-ray bursts are of particular interest. An interpretation of our observational data along with the data obtained on other telescopes is used to test the existing theoretical models of both the SN explosion, and the surrounding circumstellar medium. In 2009 we observed 30 objects; the spectra were obtained for 12 of them. We determined the types, phases after maximum, and redshifts for five SNe (SN 2009db, SN 2009dy, SN 2009dw, SN 2009ew, SN 2009ji). Based on the obtained photometric data a discovery of two more SNe was confirmed (SN 2009bx and SN 2009cb). A study of two type II supernovae in the nebular phase (SN 2008gz and SN 2008in) is finalized, four more objects (SN 2008iy, SN 2009ay, SN 2009bw, SN 2009de) are currently monitored., Comment: 12 pages, 10 figures, to be published in Astrophysical Bulletin 65, 230-237 (2010)

CCD BVRI photometry is presented for type Ia supernova 2008gy. The light curves match the template curves for fast-declining SN Ia, but the colors appear redder than average, and the SN may also be slightly subluminous. SN 2008gy is found to be located far outside the boundaries of three nearest galaxies, each of them has nearly equal probability to be the host galaxy., Comment: 6 pages, 3 figures, submitted to Variable Stars

Multiple outbursts of type Ia SNe in one galaxy present a unique opportunity to study the homogeneity of these objects. NGC 3147 is only the second known galaxy with three SNe Ia, another one is NGC 1316. We present CCD UBVRI photometry for SN Ia 2008fv and compare the light and color curves of this object with those for SNe Ia discovered earlier in NGC 3147: 1972H and 1997bq. The photometric properties of SNe 1997bq and 2008fv are nearly identical, while SN 1972H exhibits faster declining light curve., Comment: 11 pages, 6 figures, submitted to Peremennye Zvezdy (Variable Stars)

Photometric observations of three core collapse supernovae (SNe 2004ao, 2004gk and 2006gi), covering about 200 days of evolution are presented and analyzed. The photometric behaviour of the three objects is consistent with their membership of the envelope-stripped type Ib/c class. Pseudo-bolometric light curves are constructed. The corresponding measured $e$-folding times are found to be faster compared to the $^{56}$Co decay (i.e. 111.3 d), suggesting that a proportion of $\gamma$-rays increasing with time have escaped without thermalization, owing to the low mass nature of the ejecta. SN 2006gi has almost identical post maximum decline phase luminosities as SN 1999ex, and found to be similar to both SNe 1999dn and 1999ex in terms of the quasi-bolometric shape, placing it among the fast decliner Ib objects. SN 2004ao appears to fit within the slow decliner Ib SNe. SNe 2004ao and 2004gk display almost identical luminosities in the [50-100] days time interval, similar to SN 1993J. A preliminary simplified $\gamma -$ray deposition model is described and applied to the computed pseudo-bolometric light curves, allowing one to find a range in the ejecta and $^{56}$Ni masses. The optical and quasi-bolometric light curves, and the $B-V$ colour evolution of SN 2004gk are found to show a sudden drop after day 150. Correlating this fact to dust formation is premature and requires further observational evidence., Comment: Accepted for publication in The Astrophysical Journal; (11 two-columns Pages, 11 figures, 6 Tables; Scheduled for publication in April 2011)

We present new optical and near infrared (NIR) photometry and spectroscopy of the type IIP supernova, SN 2004et. In combination with already published data, this provides one of the most complete studies of optical and NIR data for any type IIP SN from just after explosion to +500 days. The contribution of the NIR flux to the bolometric light curve is estimated to increase from 15% at explosion to around 50% at the end of the plateau and then declines to 40% at 300 days. SN 2004et is one of the most luminous IIP SNe which has been well studied, and with a luminosity of log L = 42.3 erg/s, it is 2 times brighter than SN 1999em. We provide parametrised bolometric corrections as a function of time for SN 2004et and three other IIP SNe that have extensive optical and NIR data, which can be used as templates for future events. We compare the physical parameters of SN 2004et with those of other IIP SNe and find kinetic energies spanning the range of 10^50-10^51 ergs. We compare the ejected masses calculated from hydrodynamic models with the progenitor masses and limits derived from prediscovery images. Some of the ejected mass estimates are significantly higher than the progenitor mass estimates, with SN 2004et showing perhaps the most serious mass discrepancy. With current models, it appears difficult to reconcile 100 day plateau lengths and high expansion velocities with the low ejected masses of 5-6 Msun implied from 7-8 Msun progenitors. The nebular phase is studied using very late time HST photometry, along with optical and NIR spectroscopy. The light curve shows a clear flattening at 600 days in the optical and the NIR, which is likely due to the ejecta impacting on the CSM. We further show that the [Oi] 6300,6364 Angstrom line strengths of four type IIP SNe imply ejected oxygen masses of 0.5-1.5 Msun., Comment: 25 pages, 27 figures, submitted to MNRAS

CCD UBVRI photometry is presented for type IIb SN 2008ax for about 320 days. The photometric behavior is typical for core-collapse SNe with low amount of hydrogen. The main photometric parameters are derived and the comparison with SNe of similar types is reported. Preliminary modeling is carried out, and the results are compared to the observed light curves. The main parameters of the hydrodynamical models are close to those used for SN IIb 1993J., Comment: 12 pages, 8 figures, submitted to Variable Stars

We present comprehensive photometric and spectroscopic observations of the faint transient SN 2008S discovered in NGC 6946. SN 2008S exhibited slow photometric evolution and almost no spectral variability during the first nine months, implying a high density CS medium. The light curve is similar in shape to that of SN 1998S and SN 1979C, although significantly fainter at maximum light. Our quasi-bolometric lightcurve extends to 300 days and shows a tail phase decay rate consistent with that of ^{56}Co. We propose that this is evidence for an explosion and formation of ^{56}Ni (0.0015 +/- 0.0004 M_Sun). The large MIR flux detected shortly after explosion can be explained by a light echo from pre-exisiting dust. The late NIR flux excess is plausibly due to a combination of warm newly-formed ejecta dust together with shock-heated dust in the CS environment. We reassess the progenitor object detected previously in Spitzer archive images, supplementing this discussion with a model of the MIR spectral energy distribution. This supports the idea of a dusty, optically thick shell around SN 2008S with an inner radius of nearly 90AU and outer radius of 450AU, and an inferred heating source of 3000 K and luminosity of L ~ 10^{4.6} L_Sun. The combination of our monitoring data and the evidence from the progenitor analysis leads us to support the scenario of a weak electron capture supernova explosion in a super-AGB progenitor star (of initial mass 6-8 M_sun) embedded within a thick CS gaseous envelope. We suggest that all of main properties of the electron capture SN phenomenon are observed in SN 2008S and future observations may allow a definitive answer., Comment: accepted for publication in MNRAS (2009 May 7)

CCD UBVRI photometry is presented for type II SN 2004dj for about 1200 days, starting day 2 past discovery. The photometric behaviour is typical for SNe II-P, although some minor peculiarities are noticed. We compare the photometric data for the host cluster S96 before and after SN 2004dj outburst and do not find any significant changes., Comment: 12 pages, 6 figures, submitted to Variable Stars (Peremennye Zvezdy)

CCD UBVRI photometry is presented for type IIn SN 2005kd. The maximum luminosity exceeded Mv=-19.8, and SN remained brighter than -18 mag for about 400 days. While overall photometric evolution is quite similar to SN 1997cy, SN 2005kd shows a plateau at phases between 119 and 311 days past explosion, which is a unique feature for SN IIn., Comment: 8 pages, 5 figures, submitted to Variable Stars