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Context. Spider pulsars are millisecond pulsars in tight binary systems, in which a low-mass companion star is heated and ablated by the pulsar wind. Their observations allow one to study stellar evolution with formation of millisecond pulsars and physics of superdense matter in neutron stars. However, spiders are rare due to difficulties of their discovery using typical radio search techniques. The Fermi $\gamma$-ray source 4FGL J1544.2$-$2554 was recently proposed as a pulsar candidate, and its likely X-ray and optical counterparts with the galactic coordinates $l\approx344.\!\!^\circ76$, $b\approx22.\!\!^\circ59$ and the magnitude $G\approx20.6$ were found using the eROSITA and Gaia surveys. Aims. Our goals are to study whether the source is a new spider pulsar and to estimate its fundamental parameters. Methods. We performed the first optical time-series multi-band photometry of the object. We used the Lomb-Scargle periodogram to search for its brightness periodicity and fitted its light curves with a model of direct heating of the binary companion by the pulsar wind. Results. The source shows a strong brightness variability with a period of $\approx$ 2.724 h and an amplitude of $\gtrsim$ 2.5 mag, and its light curves have a single broad peak per period. These features are typical for spider pulsars. The curves are well fitted by the direct heating model, resulting in an orbit inclination of the presumed spider system of $\approx 83^\circ$, a companion mass of $\approx 0.1$ M$_\odot$, its ''day-side'' and ''night-side'' temperatures of $\approx 7200$ K and $\approx 3000$ K, a Roche-lobe filling factor of $\approx 0.65$ and a distance of $\approx 2.1$ kpc. Conclusions. Our findings suggest that 4FGL J1544.2$-$2554 is a spider pulsar. This encourages searches for the pulsar millisecond pulsations in the radio and $\gamma$-rays to confirm its nature., Comment: 6 pages, accepted for publication in Astronomy & Astrophysics

Deep neural network models have a complex architecture and are overparameterized. The number of parameters is more than the whole dataset, which is highly resource-consuming. This complicates their application and limits its usage on different devices. Reduction in the number of network parameters helps to reduce the size of the model, but at the same time, thoughtlessly applied, can lead to a deterioration in the quality of the network. One way to reduce the number of model parameters is matrix decomposition, where a matrix is represented as a product of smaller matrices. In this paper, we propose a new way of applying the matrix decomposition with respect to the weights of convolutional layers. The essence of the method is to train not all convolutions, but only the subset of convolutions (basis convolutions), and represent the rest as linear combinations of the basis ones. Experiments on models from the ResNet family and the CIFAR-10 dataset demonstrate that basis convolutions can not only reduce the size of the model but also accelerate the forward and backward passes of the network. Another contribution of this work is that we propose a fast method for selecting a subset of network layers in which the use of matrix decomposition does not degrade the quality of the final model., Comment: Increase the size of matrix pictures for better UX in PDF view

Context. Two millisecond pulsars, PSR J1513$-$2550 and PSR J2017$-$1614, with spin periods of about 2.1 and 2.3 ms were recently discovered in the radio and $\gamma$-rays and classified as black widow pulsars in tight binary stellar systems with orbital periods of about 4.3 and 2.3 h. Aims. Our goals are to reveal fundamental parameters of both systems and their binary components using multi-wavelength observations. Methods. We carried out the first time-series multi-band optical photometry of the objects with the 2.1-metre telescope of the Observatorio Astron\'omico Nacional San Pedro M\'artir, the 6.5-metre \magel-1 telescope, and the 10.4-metre Gran Telescopio Canarias. To derive the parameters of both systems, we fitted the obtained light curves with a model assuming heating of the companion by the pulsar. We also analysed archival X-ray data obtained with the XMM-Newton observatory. Results. For the first time, we firmly identified J1513$-$2550 in the optical and both pulsars in X-rays. The optical light curves of both systems have a single peak per orbital period with peak-to-peak amplitude of $\gtrsim2$ magnitudes. The J2017$-$1614 light curves are symmetric, while J1513$-$2550 demonstrates strong asymmetry whose nature remains unclear. Conclusions. We constrained the orbital inclinations, pulsar masses, companion temperatures and masses, as well as the distances to both systems. We also conclude that J2017$-$1614 may contain a massive neutron star of 2.4$\pm$0.6 M$_{\odot}$. The X-ray spectra of both sources can be fitted by power laws with parameters typical for black widow systems., Comment: 9 pages, 4 figures, Accepted for publication in A&A

An unidentified $\gamma$-ray source 4FGL J1838.2+3223 has been proposed as a pulsar candidate. We present optical time-series multi-band photometry of its likely optical companion obtained with the 2.1-m telescope of Observatorio Astron\'omico Nacional San Pedro M\'artir, Mexico. The observations and the data from the Zwicky Transient Facility revealed the source brightness variability with a period of $\approx$4.02 h likely associated with the orbital motion of the binary system. The folded light curves have a single sine-like peak per period with an amplitude of about three magnitude accompanied by fast sporadic flares up to one magnitude level. We reproduce them modelling the companion heating by the pulsar. As a result, the companion side facing the pulsar is strongly heated up to 11300$\pm$400 K, while the temperature of its back side is only 2300$\pm$700 K. It has a mass of 0.10$\pm$0.05 ${\rm M}_\odot$ and underfills its Roche lobe with a filling factor of $0.60^{+0.10}_{-0.06}$. This implies that 4FGL J1838.2+3223 likely belongs to the `spider' pulsar family. The estimated distance of $\approx$3.1 kpc is compatible with Gaia results. We detect a flare from the source in X-rays and ultraviolet using Swift archival data and another one in X-rays with the eROSITA all-sky survey. Both flares have X-ray luminosity of $\sim$10$^{34}$ erg s$^{-1}$ which is two orders of magnitude higher than the upper limit in quiescence obtained from eROSITA assuming spectral shape typical for spider pulsars. If the spider interpretation is correct, these flares are among the strongest flares observed from non-accreting spider pulsars., Comment: 10 pages, 11 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society

PSR J1641+8049 is a 2 ms black widow pulsar with the 2.2 h orbital period detected in the radio and $\gamma$-rays. We performed new phase-resolved multi-band photometry of PSR J1641+8049 using the OSIRIS instrument at the Gran Telescopio Canarias. The obtained data were analysed together with the new radio-timing observations from the Canadian Hydrogen Intensity Mapping Experiment (CHIME), the X-ray data from the Spectrum-RG/eROSITA all-sky survey, and all available optical photometric observations. An updated timing solution based on CHIME data is presented, which accounts for secular and periodic modulations in pulse dispersion. The system parameters obtained through the light curve analysis, including the distance to the source 4.6-4.8 kpc and the orbital inclination 56-59 deg, are found to be consistent with previous studies. However, the optical flux of the source at the maximum brightness phase faded by a factor of $\sim$2 as compared to previous observations. Nevertheless, the face of the J1641+8049 companion remains one of the most heated (8000-9500 K) by a pulsar among the known black widow pulsars. We also report a new estimation on the pulsar proper motion of $\approx$2 mas yr$^{-1}$, which yields a spin down luminosity of $\approx$4.87$\times 10^{34}$ ergs s$^{-1}$ and a corresponding heating efficiency of the companion by the pulsar of 0.3-0.7. The pulsar was not detected in X-rays implying its X-ray-luminosity was <3 $\times$ 10$^{31}$ erg s$^{-1}$ at the date of observations., Comment: Accepted for publication in MNRAS

We report the first radial velocity spectroscopic study of the eclipsing period bouncer SDSS J105754.25+275947.5. Together with eclipse light curve modeling, we redetermined the system parameters and studied the accretion disk structure. We confirm that the system contains a white dwarf with $M_{\mathrm{WD}}=0.83(3) M_\odot$ and an effective temperature of 11,500(400)K. The mass of the secondary is $M_2 = 0.056 M_\odot$ with an effective temperature of T$_2$=2,100K or below. The system inclination is $i=84.3(6)$. The data is in good agreement with our determination of $K_1$ = 33(4) km s$^{-1}$. We estimate the mass transfer rate as $\dot{M}=$1.9(2)$\times 10^{-11} M_\odot yr^{-1}$. Based on an analysis of the SDSS and OSIRIS spectra, we conclude that the optical continuum is formed predominantly by the radiation from the white dwarf. The contribution of the accretion disk is low and originates from the outer part of the disk. The Balmer emission lines are formed in a plasma with $\log$ $N_0$ = 12.7 [cm$^{-1}$] and a kinetic temperature of T$\sim$10,000K. The size of the disk, where the emission lines are formed, expands up to $R_\mathrm{d,out}=0.29 R_\odot$. The inner part of the emission line forming region goes down to $R_\mathrm{d,in}\approx 2 R_\mathrm{WD}$ . The Doppler tomography and trailed spectra show the presence of a hot spot and a clumpy structure in the disk, with variable intensity along the disk position angle. There is an extended region at the side opposite the hot spot with two bright clumps caused more probably by non-Keplerian motion there., Comment: 8 pages, 9 figures, accepted for publication in MNRAS

We present the results of optical spectroscopy of stellar companions to three binary millisecond pulsars, PSRs J0621$+$2514, J2317$+$1439 and J2302$+$4442, obtained with the Gran Telescopio Canarias. The spectrum of the J0621$+$2514 companion shows a blue continuum and prominent Balmer absorption lines. The latter are also resolved in the spectrum of the J2317$+$1439 companion, showing that both are DA-type white dwarfs. No spectral features are detected for the J2302$+$4442 companion, however, its broadband magnitudes and the spectral shape of the continuum emission imply that this is also a DA-type white dwarf. Based on the spectral analyses, we conclude that the companions of J0621$+$2514 and J2317$+$1439 are relatively hot, with effective temperatures $T_{\rm eff}$$=$8600$\pm$200 and 9600$\pm$2000~K, respectively, while the J2302$+$4442 companion is significantly cooler, $T_{\rm eff}$$<$6000~K. We also estimated the distance to J0621$+$2514 of 1.1$\pm$0.3 kpc and argue that its companion and the companion of J2317$+$1439 are He-core white dwarfs providing constraints on their cooling ages of $\lesssim$2 Gyr., Comment: 9 pages, 8 figures. Paper accepted to MNRAS

We present a new study of the Z~Cam-type eclipsing cataclysmic variable AY~Piscium with the aim of determining the fundamental parameters of the system and the structure of the accretion flow therein. We use time-resolved photometric observations supplemented by spectroscopy in the standstill, to which we applied our light-curve modeling techniques and the Doppler tomography method, to update system parameters. We found that the system has a massive white dwarf $M_{\rm WD}=0.90(4)$ \ms, a mass ratio $q=0.50(3)$, and the effective temperature of a secondary $T_2 = 4100(50)$~K. The system inclination is $i=74.^{\circ}8(7)$. The orbital period of the system $P_{\mathrm{orb}}=0.217320523(8)\;\mathrm{d}$ is continuously increasing with the rate of $\dot{P}_{\mathrm{orb}} = +7.6(5)\times10^{-9}$ d year$^{-1}$. The mass transfer rate varies between 2.4$\times$10$^{-10}$ M$_\odot$ year$^{-1}$ in quiescence up to 1.36$\times$10$^{-8}$ M$_\odot$ year$^{-1}$ in outburst. The accretion disk transitions from the cooler, flared, steady-state disk to a warmer state with a practically constant and relatively high disk height. The mass transfer rate is about 1.6$\times$10$^{-9}$ M$_\odot$ year$^{-1}$ in the standstill. The Balmer emission lines show a multi-component structure similar to that observed in long-orbital-period nova-like systems. Out of standstill, the system exhibits outburst bimodality, with long outbursts being more prominent. We conclude that the Balmer emission lines in AY~Psc are formed by the combination of radiation from the irradiated surface of the secondary, from the outflow zone, and from winds originating in the bright spot and the disk's inner part.

A very long term variability (VLPP), with period of 875 days, was observed in the long-term light curve of FS Aurigae in 2011. This periodicity was calculated on 6 cycles. We re-examine the periodicity with new observations over of the past 5 yrs. A total of 18 yrs of observations confirm the hypothesis of a third body perturbing in a secular way the cataclysmic variable (CV). Improvements to the model such as eccentric and inclined orbits for the third body and a binary post-Newtonian correction are considered. We confirm the VLPP of FS Aur and find the new period of 857 $\pm$ 78 days. The secular perturbations are most efficient when the mass of the third body is M=29 MJ, much less than the 50 MJ reported in 2011. We estimate the effect of the third body on the mass transfer rate and the brightness of the system. We consider alternative scenarios for the VLPP. The new data and analysis supports the hypothesis that FS Aur is a CV in a triple system., Comment: 16 pages, 5 figures

Some Cataclysmic Variables (CVs) exhibits a very long photometric period (VLPP). We calculate the properties of a hypothetical third body, initially assumed on circular--planar orbit, by matching the modelled VLPP to the observed one of four CVs studied here: {\sl LU Camelopardalis} (LU Cam), QZ Serpentis (QZ Ser), V1007 Herculis (V1007 Her) and BK Lyncis (BK Lyn). The eccentric and low inclination orbits for a third body are considered using analytical results. The chosen parameters of the binary components are based on the orbital period of each CV. The smallest corresponding semi-major axis permitted before the third body's orbit becomes unstable is also calculated. A first-order analytical post-Newtonian correction is applied, and the rate of precession of the pericentre is found, but it can not explain any of the observed VLPP. For the first time, we also estimate the effect of secular perturbations by this hypothetical third body on the mass transfer rate of such CVs. We made sure that the observed and calculated amplitude of variability was comparable too. The mass of the third body satisfying all constrains range from 0.63 to 97 Jupiter masses. Our results show further evidence supporting the hypothesis of a third body in three of these CVs, but only marginally in V1007 Her., Comment: 11 pages, 6 figures

The 840 kyr old pulsar PSR J1957+5033, detected so far only in $\gamma$- and X-rays, is a nearby and rather cool neutron star with a temperature of 0.2--0.3 MK, a distance of $\la$1 kpc, and a small colour reddening excess $E(B-V) \approx 0.03$. These properties make it an ideal candidate to detect in the optical to get additional constraints on its parameters. We thus performed the first deep optical observations of the pulsar with the 10.4-meter Gran Telescopio Canarias in the $g'$ band and found its possible counterpart with $g'=27.63\pm 0.26$. The counterpart candidate position is consistent with the X-ray coordinates of the pulsar within the 0.5 arcsec accuracy. Assuming that this is the real counterpart, we analysed the pulsar X-ray spectrum together with the derived optical flux density. As a result, we found that the thermal emission from the bulk surface of the cooling neutron star can significantly contribute to its optical flux. Our multi-wavelength spectral analysis favours the pulsar nature of the detected optical source, since it provides physically adequate parameters of the pulsar emission. We show that the optical data can provide new constraints on the pulsar temperature and distance., Comment: 7 pages, 3 figures, published in MNRAS

Context. The eclipsing close binary UU Cas is an interacting massive double-periodic system with a gainer star partly hidden in an accretion disk. Aims. In order to study the physics of the accretion process in greater detail, along with the structure and dynamics of the circumstellar matter in the system, we supplement our previous results obtained from photometry with an analysis of the spectra of UU Cas. Methods. We collected all available spectra used in previous publications on UU Cas and we acquired new ones. The method of disentangling was applied to this set of spectra spanning the years 2008-2021. The orbital parameters were disentangled and a fit of the separated component spectra by synthetic ones has been used to determine the physical parameters of the component stars. We compared the results to models of the evolution of interacting binaries. Results. We found that in addition to the dominant role of the donor star and a weak contribution of the gainer, the line profiles are strongly influenced by the circumstellar matter. The absorption lines reveal a presence of a disk wind emanating above the orbital plane. The variability of H{\alpha} emission yields evidence of changes in the structure of the circumstellar matter on a timescale of several orbital periods.

We present a photometric and spectroscopic study of HD 50526, an ellipsoidal binary member of the group Double Periodic Variable stars. Performing data-mining in photometric surveys and conducting new spectroscopic observations with several spectrographs during 2008 to 2015, we obtained orbital and stellar parameters of the system. The radial velocities were analyzed with the genetic PIKAIA algorithm, whereas Doppler tomography maps for the H$\alpha$ and H$\beta$ lines were constructed with the Total Variation Minimization code. An optimized simplex-algorithm was used to solve the inverse-problem adjusting the light curve with the best stellar parameters for the system. We find an orbital period of $6.701 \pm 0.001 ~\mathrm{d}$ and a long photometric cycle of $191 \pm 2 ~\mathrm{d}$. We detected the spectral features of the coldest star, and modeled it with a $\log{g} = 2.79 \pm 0.02 ~\mathrm{dex}$ giant of mass $1.13 \pm 0.02 ~\mathrm{M_{\odot}}$ and effective temperature $10500 \pm 125 ~\mathrm{K}$. In addition, we determine a mass ratio $q= 0.206 \pm 0.033$ and that the hot star is a B-type dwarf of mass $5.48 \pm 0.02 ~\mathrm{M_{\odot}}$. The $V$-band orbital light curve can be modeled including the presence of an accretion disk around the hotter star. This fills the Roche lobe of the hotter star, and has a radius $14.74 \pm 0.02 ~\mathrm{R_{\odot}}$ and temperature at the outer edge $9400 ~\mathrm{K}$. Two bright spots located in the disk account for the global morphology of the light curve. The Doppler tomography maps of H$\alpha$ and H$\beta$, reveal complex structures of mass fluxes in the system., Comment: 16 pages with 14 figures

Context: We present a new study of the eclipsing cataclysmic variable CzeV404 Her (Porb = 0.098 d) that is located in the period gap. Aims: This report determines the origin of the object and the system parameters and probes the accretion flow structure of the system. Methods: We conducted simultaneous time-resolved photometric and spectroscopic observations of CzeV404 Her. We applied our light-curve modelling techniques and the Doppler tomography method to determine the system parameters and analyse the structure of the accretion disk. Results: We found that the system has a massive white dwarf M_WD = 1.00(2) M_sun a mass ratio of q = 0.16, and a relatively hot secondary with an effective temperature T_2 = 4100(50) K. The system inclination is i = 78.8{\deg}. The accretion disk spreads out to the tidal limitation radius and has an extended hot spot or line region. The hot spot or line is hotter than the remaining outer part of the disk in quiescence or in intermediate state, but does not stand out completely from the disk flux in (super)outbursts. Conclusions: We claim that this object represents a link between two distinct classes of SU UMa-type and SW Sex-type cataclysmic variables. The accretion flow structure in the disk corresponds to the SW Sex systems, but the physical conditions inside the disk fit the behaviour of SU UMa-type objects.

We analysed a wealth of optical spectroscopic and photometric observations of the bright (V=11.9) cataclysmic variable BG Tri. TheGaiaDR2 parallax gives a distance d=334(8)pc to the source, making the object one of the intrinsically brightest nova-like variables seen under a low orbital inclination angle. Time-resolved spectroscopic observations revealed the orbital period of P(orb)=3.h8028(24). Its spectroscopic characteristics resemble RW Sex and similarnova-like variables. We disentangled the H alpha emission line into two components, and show that one component forms on the irradiated face of the secondary star. We suggest that the other one originates at a disc outflow area adjacent to the L3 point., Comment: Accepted for publication in MNRAS, 11 pages, 10 figures

We report detection of PSR B0656$+$14 with the Gran Telescopio Canarias in narrow optical $F657$, $F754$, $F802$, and $F902$ and near-infrared $JHK_s$ bands. The pulsar detection in the $K_s$ band extends its spectrum to 2.2 $\mu$m and confirms its flux increase towards the infrared. We also present a thorough analysis of the optical spectrum obtained by us with the VLT. For a consistency check, we revised the pulsar near-infrared and narrow-band photometry obtained with the \textit{HST}. We find no narrow spectral lines in the optical spectrum. We compile available near-infrared-optical-UV and archival 0.3-20keV X-ray data and perform a self-consistent analysis of the rotation phase-integrated spectrum of the pulsar using unified spectral models. The spectrum is best fitted by the four-component model including two blackbodies, describing the thermal emission from the neutron star surface and its hot polar cap, the broken power-law, originating from the pulsar magnetosphere, and an absorption line near $\sim$0.5 keV detected previously. The fit provides better constraints on the model parameters than using only a single spectral domain. The derived surface temperature is $T_{NS}^{\infty}=7.9(3)\times10^5$K. The intrinsic radius (7.8-9.9 km) of the emitting region is smaller than a typical neutron star radius (13km) and suggests a nonuniform temperature distribution over the star surface. In contrast, the derived radius of the hot polar cap is about twice as large as the `canonical' one. The spectrum of the nonthermal emission steepens from the optical to X-rays and has a break near 0.1 keV. The X-ray data suggest the presence of another absorption line near 0.3keV., Comment: 18 pages, 9 figures, Accepted for publication in MNRAS