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This work of thesis aims to study the properties of the recurrent nova RS Ophiuchi, whose latest outburst phase was observed in August 2021. RS Ophiuchi is a binary system composed of a red giant star and a CO white dwarf (WD). These stars are close enough to have the transfer of matter from the red giant to the WD. The accretion of this matter on the surface of the WD gives rise to recurrent releases of energy by a thermonuclear runaway. Simulations of the nova RS Ophiuchi were made with MESA (Modules for Experiments in Stellar Astrophysics) star module as a part of the NuGrid (Nucleosynthesis Grid) collaboration’s collection of software tools for simulations. Two different simulations were made for the WD profile with and without convective boundary mixing. For each WD profile, WD models for different evolutionary paths were made, resulting in WD models with different masses of the accreted shells. For the logarithmic luminosity of the RS Ophiuchi, a value of log10 L L⊙ = 1.867, has been obtained, and comparison with the logarithmic luminosity of models in plots of constant WD Roche lobe radius brought me to the conclusion that RS Ophiuchi has a greater mass of the accreted envelope than most models. Models with logarithmic luminosity close to the one of RS Ophiuchi of both profiles have both pp-chain, and CNO cycles ignited in their accreted envelope, confirming that these models are good models of the nova RS Ophiuchi.

We modelled optical light curves of Sco~X-1 obtained by the Kepler space telescope during K2 mission. Modelling was performed for the case of the strong heating of the optical star and accretion disc by X-rays. In the considered model the optical star fully filled its Roche lobe. We investigated the inverse problem in wide ranges of values of model parameters and estimated following parameters of Sco X-1: the mass ratio of components $q=M_x/M_v=3.6$ ($3.5-3.8$), where $M_x$ and $M_v$ were masses of the neutron and optical stars correspondingly, the orbital inclination was $i=30^{\circ}$ ($25^{\circ}-34^{\circ}$). In the brackets uncertainties of parameters $q$ and $i$ were shown, they originated due to uncertainties of characteristics of the physical model of Sco X-1. The temperature of non-heated optical star was $T_2 = 2500-3050$ K, its radius was $R_2=1.25R_{\odot}=8.7\times 10^{10}$ cm, and its bolometric luminosity was $L_{bol}=(2.1-4.6)\times 10^{32}$ erg s$^{-1}$. The mass of the star was $M_v\simeq 0.4M_{\odot}$. The contribution of the X-ray heated accretion disc dominated in the total optical emission of Sco~X-1. The transition between low and high states occurred due to the increase of X-ray luminosity by a factor $2-3$., 18 pages, 17 figures, MNRAS accepted

We report the discovery of a rare close binary system, SMSS J160639.78-100010.7, comprised of a magnetic white dwarf with a field of about 30 MG and a brown dwarf. We measured an orbital period of 92 min which is consistent with the photometric period. Minimum and maximum light occur at the orbital quadratures Phi=0.25 and 0.75, respectively, and cannot be caused by reflection on the brown dwarf, but, instead, by a spot on the synchronously rotating magnetic white dwarf. The brown dwarf does not fill its Roche lobe and the system may be in a low-accretion state or, more likely, in a detached state following episodes of mass transfer. SMSS J160639.78-100010.7 is the nearest known magnetic white dwarf plus brown dwarf system., Comment: Accepted for publication in MNRAS Letters

We study the initial conditions of a common envelope (CE) event resulting in a stellar merger. A merger's dynamics could be understood through its light curve, but no synthetic light curve has yet been created for the full evolution. Using the Smoothed Particle Hydrodynamics (SPH) code StarSmasher, we have created three-dimensional (3D) models of a 1.52 $M_\odot$ star that is a plausible donor in the V1309 Sco progenitor. The integrated total energy profiles of our 3D models match their initial one-dimensional (1D) models to within a 0.1 per cent difference in the top 0.1 $M_\odot$ of their envelopes. We have introduced a new method for obtaining radiative flux by linking intrinsically optically thick SPH particles to a single stellar envelope solution from a set of unique solutions. For the first time, we calculated our 3D models' effective temperatures to within a few per cent of the initial 1D models, and found a corresponding improvement in luminosity by a factor of $\gtrsim10^6$ compared to ray tracing. We let our highest resolution 3D model undergo Roche-lobe overflow with a 0.16 $M_\odot$ point-mass accretor ($P\simeq1.6$ days) and found a bolometric magnitude variability amplitude of $\sim0.3$ -- comparable to that of the V1309 Sco progenitor. Our 3D models are, in the top 0.1 $M_\odot$ of the envelope and in terms of total energy, the most accurate models so far of the V1309 Sco donor star. A dynamical simulation that uses the initial conditions we presented in this paper can be used to create the first ever synthetic CE evolution light curve., 13 pages, 7 figures, 3 tables. Accepted for publication in MNRAS

HL Draconis (HL Dra) is an oscillating eclipsing binary with an orbital period of 0.944276 d. By analysing the light curves observed with the Transiting Exoplanet Survey Satellite (TESS), it has been detected that HL Dra is an Algol-like binary system with a mass ratio of 0.361, where the radius filling factor (=r/RL) of the primary and secondary component is $87\, {{\ \rm per\ cent}}$ and $98\, {{\ \rm per\ cent}}$, respectively. The secondary component is almost filling its critical Roche lobe, but not entirely. The absolute parameters of the component are estimated in this paper. Both the variable O’Connell effect and the existence of superflares indicate that the secondary should have strong magnetic activities. It is discovered that the O − C curve shows a sinusoidal variation with a period of 129.88 yr. This cyclic change might be caused by the effects of the light travel time as a result of the presence of a cool red dwarf third body. The correlations between the changes of the O − C diagrams and the variable O’Connell effect during TESS observations might be caused by the magnetic activity of the secondary (i.e. the Applegate mechanism). After removal of the binary model, a total of 252 pulsation frequencies are detected from the high-precision photometric data of TESS, including 28 multiplets of tidally split frequencies. We identify two radial modes, 21 non-radial p-modes and three non-radial f-modes from the possible independent frequencies. All of these features reveal that HL Dra is a very interesting system for further investigations of binary formation and evolution, and for tidal interactions on stellar pulsations and on magnetic activities.

We present LAMOST J0140355+392651 (hereafter J0140), a close ($P_{\rm orb} = 3.81$ hours) binary containing a bloated, low-mass ($M \approx 0.15 M_{\odot}$) proto-white dwarf (WD) and a massive ($M\approx 0.95\,M_{\odot}$) WD companion. The system's optical light curve is dominated by large-amplitude ellipsoidal variability but also exhibits additional scatter, likely driven by pulsations. The proto-WD is cooler ($T_{\rm eff} = 6800\pm 100$ K) and more puffy ($\log\left[g/\left({\rm cm\,s^{-2}}\right)\right]=4.74\pm0.07$) than any known extremely low mass (ELM) WD, but hotter than any known cataclysmic variable (CV) donor. It either completely or very nearly fills its Roche lobe ($R/R_{{\rm Roche\,lobe}}=0.99\pm0.01$), suggesting ongoing or recently terminated mass transfer. No dwarf nova-like outbursts have been observed. The spectrum is dominated by the proto-WD but shows tentative hints of H$\alpha$ emission, perhaps due to accretion onto the massive WD. The properties of the system are well-matched by MESA binary evolution models of CVs with donors that underwent significant nuclear evolution before the onset of mass transfer. In these models, the bloated proto-WD is either still losing mass via stable Roche lobe overflow or was doing so until very recently. In either case, it is evolving toward higher temperatures at near-constant luminosity to become an ELM WD. If the system is detached, mass transfer likely ended when the donor became too hot for magnetic braking to remain efficient. Evolutionary models predict that the binary will shrink to $P_{\rm orb}\lesssim 10$ minutes within a few Gyr, when it will either merge or become an AM CVn binary. J0140 provides an observational link between the formation channels of CVs, ELM WDs, detached ultracompact WD binaries, and AM CVn systems., Comment: 19 pages, 14 figures. Accepted to MNRAS

GG Carinae is a binary whose primary component is a B[e] supergiant. Using photometric data from TESS, ASAS, OMC, and ASAS-SN, and spectroscopic data from the Global Jet Watch to study visible He\,I, Fe\,II and Si\,II emission lines, we investigate the short-period variations which are exhibited in GG Car. We find a hitherto neglected periodicity of $1.583156\pm0.0002$\,days that is present in both its photometry and the radial velocities of its emission lines, alongside variability at the well-established $\sim$31-day orbital period. We find that the amplitudes of the shorter-period variations in both photometry and some of the emission lines are modulated by the orbital phase of the binary, such that the short-period variations have largest amplitudes when the binary is at periastron. There are no significant changes in the phases of the short-period variations over the orbital period. We investigate potential causes of the 1.583-day variability, and find that the observed period agrees well with the expected period of the $l=2$ f-mode of the primary given its mass and radius. We propose that the primary is periodically pulled out of hydrostatic equilibrium by the quadrupolar tidal forces when the components are near periastron in the binary's eccentric orbit ($e=0.5$) and the primary almost fills its Roche lobe. This causes an oscillation at the $l=2$ f-mode frequency which is damped as the distance between the components increases., Comment: Accepted for publication in MNRAS. 14 pages, 14 figures

Stars located closely to supermassive black holes (SMBHs) can, under certain conditions, form close binary systems with the SMBHs, in which the star may fill the Roche lobe and intensive accretion of stellar matter onto the SMBH is possible. In this paper, the evolution of star + SMBH binary systems is studied under the assumption that the black hole mainly accretes the matter from the companion star. The calculations considered all the processes that determine the evolution of ordinary binary systems, as well as the irradiation of a star by a hard radiation flux arising from the accretion of its matter onto the SMBH. The absorption of the external radiation flux in the stellar envelope was calculated through the same formalism that is used to calculate the opacity of stellar matter. In addition, it was assumed that if the characteristic time of mass exchange is less than the thermal time of the star, the exchange between the orbital angular momentum of the system and the angular momentum of the matter flowing to the SMBH does not take place. The numerical simulations performed in our previous studies showed that, within the adopted assumptions, there are three possible evolution types of such a binary system, depending on the masses of the SMBH and the star, as well as on the initial distance of the star from the SMBH. The first type of the evolution results in the destruction of the star. This is the only scenario that takes place for low-mass main sequence (MS) stars with masses below $$ \sim {\kern 1pt} 1\,{{M}_{ \odot }}$$ , even if the SMBH mass is relatively small, and the initial distance of the star from the SMBH is large. Massive MS stars are destroyed as well, if the SMBH mass is large and the initial distance of the star from the SMBH is sufficiently small. The second type of the evolution may take place for massive MS stars that are initially located farther from the SMBH than in the first scenario. In this case, the massive star fills its Roche lobe during the evolutionary expansion, after which a stage of intensive exchange of matter begins. A characteristic property of the evolution of the second type is an increase in the orbital period of the system with time. As a result, after the stage of intensive loss of matter, the star “retreats” under the Roche lobe. The remnant of the star will remain as a white dwarf and may end up at a fairly large distance from the SMBH. The third type of the evolution may occur for massive MS stars that are initially located even farther from the SMBH than in the second variant, as well as for evolved massive stars. In this case, conservative mass exchange accompanied by intense stellar wind leads to the fact that the star moves away from the SMBH without filling its Roche lobe at all. In this paper, we thoroughly examine the first type of the evolution, which results in the destruction of the star. According to the calculation results, the greater the mass of the SMBH, the greater the maximum mass $${{M}_{{\max}}}$$ of stars that can be destroyed. For black holes of intermediate mass, $$({{10}^{3}}{-} {{10}^{5}})\,{{M}_{ \odot }}$$ , the $${{M}_{{\max}}}$$ value is relatively small and amounts to (2–9) $${{M}_{ \odot }}$$ . For SMBHs with a mass of $${{10}^{6}}\,{{M}_{ \odot }}$$ , $${{M}_{{\max}}}$$ is close to 25 $${{M}_{ \odot }}$$ . For massive SMBHs with masses of $$({{10}^{7}}{-} {{10}^{9}})\,{{M}_{ \odot }}$$ , $${{M}_{{\max}}}$$ exceeds 50 $${{M}_{ \odot }}$$ . If the mass of the star is lower than $${{M}_{{\max}}}$$ and the initial degree of filling of the Roche lobe $$D$$ is greater than the boundary value $${{D}_{{{\text{destr}}}}}$$ , the star will be destroyed, while at $$D < {{D}_{{{\text{destr}}}}}$$ it will move away from the SMBH and may avoid destruction. The greater the mass of the SMBH, the lower the $${{D}_{{{\text{destr}}}}}$$ , value for a star of a given mass. The character of the evolution of a star + SMBH system before the destruction of the star depends on the stellar mass. For stars with masses $$M \lesssim 1\,{{M}_{ \odot }}$$ , destruction begins immediately after the filling of the Roche lobe and a corresponding rapid increase in the rate of matter loss. For more massive stars, the filling of the Roche lobe is followed by the evolutionary phase with a relatively low rate of matter loss. As the semimajor axis of the orbit decreases to a certain value, this rate increases rapidly, which leads to an increased degree of irradiation of the star and its destruction. At the initial phase of the destruction, the star’s rate of matter loss grows the faster, the greater the mass of the SMBH, the smaller the initial mass of the star, and the closer the star is to the SMBH at the initial moment. The characteristic times of increase in $$\dot {M}$$ by three orders of magnitude at the beginning of the destruction phase vary from tens to thousands of years, depending on the masses of the star and the SMBH.

Ellipsoidal variables present light-curve modulations caused by stellar distortion, induced by tidal interaction with their companions. An analytical approximated model of the ellipsoidal modulation is given as a discrete Fourier series by Morris and Naftilan 1993 (MN93). Based on numerical simulations using the PHOEBE code we present here updated amplitudes of the first three harmonics of the model. The expected amplitudes are given as a function of the mass ratio and inclination of the binary system and the fillout factor of the primary---the ratio between the stellar radius and that of its Roche lobe. The corrections can get up to 30% relative to the MN93 model for fillout factors close to unity. The updated model can be instrumental in searching for short-period binaries with compact-object secondaries in large data sets of photometric light curves. As shown in one OGLE light-curve example, the minimum mass ratio can be obtained by using only the amplitudes of the three harmonics and an estimation of the stellar temperature. High enough amplitudes can help to identify binaries with mass ratios larger than unity, some of which might have compact companions., Comment: 13 pages, 6 figures