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The results of infrared observations of the two Be stars X Per and V725 Tau, which are the optical components of X-ray binary systems, obtained in 1994–2016 are presented. The observations cover Be-star phases as well as shell phases. The data analysis shows that the radiation observed from the binaries at 1.25, 3.5, and 5 μm can be explained as the combined radiation from the optical components and variable sources (shells/disks) that emit as blackbodies (BBs). Emission from a source with the color temperature T c ~1000−1500 K was detected for X Per at λ ≥ 3.5 μm. The highest IR-brightness variation amplitudes for X Per were 0.9−1.2 m (JHK magnitudes) and ~1.45 m (LM magnitudes); for V725 Tau, they were 1.1−1.4 m and ~1.7 m (L magnitudes). The parameters of the optical components and interstellar extinction during the Be phases were estimated: the color excesswasE(B−V) = 0.65±0.08 m and 0.77 ± 0.03 m for X Per and V725 Tau, respectively. Light from the variable sources (disks/shells) was distinguished and their color temperatures, radii, and luminosities estimated for different observation epochs in a BB model. The variations of the binaries’ IR brightness and colors are shown to be due to changing parameters of the variable sources. The mean color temperature of the cool source (disk/shell) and the mean radius and mean luminosity of X Per are 9500± 2630 K, (35 ± 10) R⊙, and (9100± 540) L⊙. For V725 Tau, these parameters are 6200 ± 940 K, (27 ± 6) R⊙, and (980 ± 420) L⊙. The 1.25–5 μm radiation from X Per at different epochs can be represented as a sum of contributions from at least three sources: the optical component and two objects emitting as BBs. To reproduce the 1.25–3.5 μm radiation from V725 Tau, two components are sufficient: the optical component and a single variable BB object. For both binary systems, orbital variations of the IR brightness can be noted near the Be-star phase. The amplitudes of the J-band variations of X Per and V725 Tau are about 0.3 m and 0.1 m , respectively.

The results of JHKLM photometry of two carbon stars are presented: the irregular variable NQ Cas and the Mira star BD Vul. Data on the mean fluxes supplemented with mid-IR observations with the IRAS, AKARI, andWISE satellites are used to compute spherically symmetrical model dust envelopes for the stars, consisting of particles of amorphous carbon and silicon carbide. The optical depth in the visible for the comparatively cool dust envelope of BD Vul, with a dust temperature at its inner boundary T1 = 610 K, is fairly low: τV = 0.13. The dust envelope of NQ Cas is appreciably hotter (T1 = 1550 K), and has τV = 0.32. The estimated mass-loss rates are 1.5 × 10−7M⊙/yr for NQ Cas and 5.9 × 10−7M⊙/yr for BD Vul.

Long-term JHKLM photometric measurements of the oxygen Mira variables RU Her and RS Vir are presented. Variations of the brightnesses and colors of these stars over the observation period are analyzed, and master light curves and color indices of these stars are derived. A linear trend was present in the mean infrared brightness of RS Vir on a time scale of ∼6000 day, possibly related to changes in the dust shell of the Mira. The results of model calculations of spherically symmetric dust shells of stars based on mean-flux data supplemented by observations from the IRAS and AKARI satellites in the intermediate- and far-IR are presented. The visual optical depth of the dust shell of RU Her, which has a temperature at its inner boundary T 1 = 590 K, is quite low: τ V = 0.33. The dust shell of RS Vir is much cooler (T 1 = 410 K), and has τ V = 0.77. The estimated mass-loss rate of RU Her is 6.2 × 10−7 M ⊙/yr, while the mass-loss rate of RS Vir is 7.1 × 10−7 M ⊙/yr.

We present the results of our infrared J H K L photometry of the Seyfert galaxy NGC 4151 during its active period in 1995–2011. The variable IR source was still in its active state in 2011, though its observed luminosity had almost halved compared to the maximum of 1995–1996. If the “cool” component of the galaxy’s variable source is a dust shell heated with the central “hot” source, its optical depth at 1.25 µm varied from 0.3 to almost 1.0, its temperature from 700 to 950 K, its size from 20 to 40 pc, and its mass from 2 to 40M⊙ during our observations. A component with a period of 317 ± 5 days can be revealed in the flux variations observed in 1994–2011.

We present JHKLM photometry of the carbon stars ST And and T Lyn acquired in 2000–2010. Along with brightness variations due to pulsations, changes on timescales of 2000–3000 days are also observed. Our combined light curves can be satisfactorily represented with light elements derived from visual observations, but the maxima are delayed relative to the calculated times. A color-index analysis demonstrates that the dust shell of ST And is fairly weak, and is manifest only episodically, while the presence of hot dust was always detected for T Lyn. These results confirm models of spherically symmetric stellar dust shells based on mean-flux data, supplemented with observations in the intermediate IR from the IRAS and AKARI satellites. The visual optical depth of the relatively cool dust shell of ST And assuming a dust temperature at the inner edge of T 1 = 510 K is very low: τ V = 0.047. The dust shell of T Lyn is considerably hotter (T 1 = 940 K), with τ V = 0.95. We estimate the mass-loss rate to be 1.8 × 10−7 M ⊙/year for ST And and 3.7 × 10−7 M ⊙/year for T Lyn.

Long-term (1984–2008) JHKLM photometry for 254 objects is presented. The observations were carried out in the standard JHKLM photometric system using an original method and a modern IR photometer designed and built at the Sternberg Astronomical Institute. Our program of studies included searches for and studies of relatively hot circumstellar dust envelopes. The most important results obtained using these observations include the following. We have detected relatively hot dust envelopes in a number of objects for the first time, including the RCB star UV Cas, RX Cas, several classical symbiotic stars, etc. A model has been calculated for the dust envelope of FG Sge, which formed around the star as a result of several successive cycles of dust condensation beginning in Autumn 1992. Several dust-condensation episodes have been traced in the envelopes of symbiotic systems (CH Cyg, V1016 Cyg, HM Sge, etc.), as well as the role of the hot component in the formation of the dust envelopes. We have established from variations of the IR emission that the cool components in the symbiotic novae V1016 Cyg and HM Sge, and possibly CH Cyg, are Miras. The binarity of V1016 Cyg and HM Sge has also been firmly established. The variability of a whole series of object has been studied, including the stellar components of close binary systems and several dozen Mira and semi-regular variables. The ellipsoidality of the components in the RX Cas system (a prototype W Ser star) and the cool component in the symbiotic systems CI Cyg and BF Cyg has been firmly established. We have obtained the first IR light curve for the eclipsing system V444 Cyg (WN5+O6), and determined the wavelength dependence of the obtained parameters of the WN5 star. Analysis of the IR light curves of several novae indicate the condensation of dust envelopes in the transition periods of Cygnus 1992, Aquila 1993, and Aquila 1995. The IR light curve of R CrB has been obtained over a long period and analyzed. IR observations of the nova-like variable V4334 Sgr have been carried out over four years, over which the star passed through four stages during its motion along its post-AGB evolutionary track; the star’s bolometric flux and optical depth of its dust envelope have been estimated, and the structure and mass of the dust layer determined. We have analyzed the IR variability of the symbiotic star V407 Cyg over 14 years, and found its cool component to be a Mira with a period of 745 days. The observed pulsations and trend are associated with the luminosity and temperature variations of the Mira, as well as the optical depth of the dust envelope. The size of the dust grains and mass-loss rate of the Mira have been determined. We have obtained JHKL light curves for the Seyfert galaxy NGC 4151 over 23 years. The IR brightness of the galaxy grew from 1985 through 1996 (by ∼0.9 m at 1.25 µm, ∼1 m at 1.65 µm, ∼1.1 m at 2.2 µm, and ∼1.3 m at 3.5 µm), while the galaxy simultaneously reddened. The “cool” variable source in NGC 4151 was still in the active state in 1998, although its luminosity had decreased by approximately 15%–20%. If the “cool” component of the variable source in this galaxy is a dust envelope heated by the central “hot” source, it should be optically thin to the radiation of this source: its mean optical depth is in the range 0.05–0.15. Emission from dust particles heated to temperatures of 600–800 K was observed in the near IR at a distance of several parsecs from the nucleus during the period of activity in 1995–1998; the inferred mass of emitting dust was 5–20 M ⊙. In 1994–2003, we observed a tendency for NGC 4151 to become bluer at 1.25–1.65 µm while simultaneously reddening at 2.2–3.5 µm. Beginning in Autumn 2000, the galaxy began to emerge from a minimum, which lasted from March 2000 through April 2001 in the IR; a flare of the galactic nucleus was observed and followed in detail in the IR in this same period. We confirm the IR variability of the nucleus of the Seyfert galaxy NGC 1068, which can be located in various stages of activity. The variability of NGC 1068 is associated with a complex source. A periodic component has been detected in the J brightness variations of the oxygen Mira V2108 Oph; we have shown that this star is immersed in a fairly dense dust envelope, and have calculated amodel for this envelope. We have calculated an (axially symmetrical) dust-envelope model for the carbon semi-regular variable RWLMi with a density distribution characteristic for the “superwind” stage. This envelope model is able to reproduce the observed fluxes over the entire observable spectrum, and displays a good agreement with the observational data. The three hot supergiants V482 Cas, QZ Sge, and HD 338926 may be variable in the IR. Long-term photometry of eight planetary nebulae in the near IR (1.25–5 µm) has enabled us to firmly establish the IR brightness and color variability of these nebulae on time scales from several tens of days to six-to-eight years. We have analyzed long-term JK photometry of the X-ray binary Cyg X-1 (V1357 Cyg). Periodicity with a characteristic time scale of ∼11.5 years is visible in the JK brightness variations of Cyg X-1 in 1984–2007, possibly due to periodic variations of the temperature, radius and luminosity of the optical component of the binary with P ∼11.5 yr. Fourteen-year IR light curves of five RV Tau stars (R Sge, RV Tau, AC Her, V Vul, and R Sct) and the yellow supergiant and protoplanetary-nebula candidate V1027 Cyg have been analyzed. A spherically symmetrical dust-envelope model has been calculated for V1027 Cyg.

We present JHKLM photometry obtained in 1984–2009 for the RCB stars UV Cas and SU Tau. No major fadings characteristic of RCB stars were detected during the observations of UV Cas, while two events of this kind occurred for SU Tau. The observed flux and color-index variations can be explained with a changing dust concentration in the line of sight, and possibly variations of the stellar temperature. We use the measured fluxes, supplemented with observations in the intermediate IR, to compute spherically symmetric dust-shell models for the stars. The mass-loss rate is estimated to be 1.7 × 10−6M⊙ yr−1 for UV Cas and 4.1 × 10−6M⊙ yr−1 for SU Tau.

Results of JHKLM photometry for the protoplanetary nebula candidate V1027 Cyg obtained in 1991–2008 are reported. In all bands, the brightness variations did not exceed 0.2m. Estimated linear trends demonstrate no significant changes in the mean brightness and color indices of the object, with the possible exception of the L-M color index, which showed a small decrease. A search for possible periodicities in the brightness variations yielded the most probable period of 237d. A model for a spherically-symmetric dust shell has been calculated based on the photometric results supplemented with data on the mid- and far-infrared fluxes. The estimated mass-loss rate of the star is 1.3 × 10−5M⊙/year.

The results of JHKLM photometry of the symbiotic star CH Cyg are presented. These demonstrate that, in Autumn 2006, the state of maximum near-IR brightness observed in 2003–2006 was replaced by a sharp brightness decline in all wavebands. One possible explanation is a sharp increase in the density of circumstellar dust envelope. The JHKLM photometry data together with ISO far-IR flux measurements are used to calculate spherically symmetric dust-envelope models for the maximum and minimum brightness states. The optical depth, expansion rate, and mass-loss rate of the envelope are calculated for both states, as well as an upper limit for the mass of the central source. Comparison with earlier models suggests that the rate of growth of the envelope optical depth and the mass-loss rate by the star are accelerating with time.

We present the results of JHKLM photometry of the oxygen Mira variable V2108 Oph acquired in 2000–2004. The period of brightness variations is refined (570 ± 3 days), and light and color curves in the near-IR are presented. The mean fluxes, color temperatures, and sizes for two blackbodies representing the combined radiation of the star and dust shell at minimum and maximum brightness are estimated. Additional IRAS data were used to compute a model with a spherically symmetric dust shell of silicate grains; the best-fit model has a radius for its inner boundary of 2.4 × 1014 cm, a dust temperature at this boundary of 1150 K, an optical depth of the shell at 0.55 µm of 16.8, and implies a distance to the star of 980 pc. We estimate the mass-loss rate for V2108 Oph to be 1.2 × 10−5 M ⊙/yr.

We have developed an axisymmetric model for the dust envelope of the carbon star RW LMi with a density distribution typical for the superwind stage using JHKLM photometric data obtained in 1997–2003, supplemented by flux data at optical, mid-IR, and far-IR wavelengths. In contrast to earlier spherically-symmetric models, the model is able to reproduce the observed fluxes in all observed wavelength ranges, and provides a good agreement with the observational data. The estimated mass-loss rate is \(\dot M = 1.2 \times 10^{ - 5} M_ \odot /yr\). The computed brightness distribution of the envelope in the near-IR is in satisfactory agreement with high-resolution observations, while the optical size is considerably larger than is observed.

Our analysis of JHKLM photometric data obtained in 1978–2003 for the CH Cyg system shows that the “local” dust envelope that formed in the system in 1986 and reached its highest column density in 1996 had largely dispersed by mid-2001, so that the observed brightness of the system’s red giant has returned to its pre-1985 level. The giant’s spectral type varied in the range M6.5–M7.5 in 2001–2003. The optical depth of the dust envelope at 1.25 µm was τ(J)≈0.83 near JD 2450090. The increase in the dust envelope’s optical depth was approximately a factor of 2.3 slower than the decrease. The envelope of CH Cyg can be pictured as a “stationary” dust cloud with an optical depth at λ=1.25 µm of ∼0.4 and a dust-grain temperature of ∼750–800 K. There was probably an injection of matter into this cloud toward the end of 1985, initiating the condensation of dust grains. The optical depth began to increase and, by 1991, the dust envelope was transformed from a cloud into a local, almost spherically-symmetric envelope with a grain temperature of 750–800 K. Its optical depth reached its maximum in 1996, after which the local envelope began to disperse, becoming a cloud again by 2001. The detected 4000-day variability of the JHK brightness of CH Cyg is in good agreement with a model with an eclipsing binary consisting of two cool giants with effective temperatures differing by approximately 100 K, a luminosity ratio of L(M7)/L(M6)∼6.8, and a radius ratio of R(M7)/R(M6)∼3.6. The orbital ephemeris is given by JD (Min I)=2444180+4000E.

Optical and infrared photometric observations of the classical symbiotic binary Z And obtained in quiescent and active phases in 1999–2002 are analyzed. RI photometric data from the literature are used to estimate the parameters of the binary system’s components. The data as a whole suggest that the hot compact component expands and the emission measure of the surrounding nebula grows during the flare. Possible interpretations of the flare based on several mechanisms are considered.

We use JHKLM photometric data obtained in 1998–2001 to model the dust envelope of the unique object FG Sge, which formed around the star after several consecutive cycles of dust condensation beginning in Autumn 1992. Models with a spherically symmetric, extended envelope consisting of a mixture of spherical particles of amorphous carbon and silicon carbide with an MRN size distribution were fitted to match the mean observed spectral energy distributions of FG Sge during brightness maximum and minimum after 1998 for two values of the luminosity and effective temperature of the central star. The stellar-wind parameters and mass-loss rate have been estimated in each case. The observational data for the brightness maximum and minimum cannot be described by models with a fixed luminosity or fixed distance to the star. This is a consequence of the object’s unusual behavior, with synchronous flux decreases in all the observed bands. The inability of the model to adequately describe the minimum-brightness state is probably associated with the abrupt disruption of the spherical symmetry of the envelope due to the formation of a small, dense dust cloud in the line of sight.

Our analysis of many years of infrared photometry of the unique object FG Sge indicates that the dust envelope formed around the supergiant in August 1992 is spherically symmetrical and contains compact, dense dust clouds. The emission from the spherically symmetrical dust envelope is consistent with the observed radiation from the star at 3.5–5 µm, and the presence of the dust clouds can explain the radiation observed at 1.25–2.2 µm. The mean integrated flux from the dust envelope in 1992–2001 was ∼(1.0±0.2)×10−8 erg s−1cm−2. The variations of its optical depth in 1992–2001 were within 0.5–1.0. The maximum density of the dust envelope was recorded in the second half of 1993 and corresponded to mean optical depths as high as unity. Several times in the interval from 1992 to 2001, the dusty material of the envelope partially dissipated and was then replenished. For example, the optical depth of the dust cloud at λ=1.25 µm during the last brigthness minimum in the J band was τ1.25≈4.3, which is much higher than the optical depth of the dust envelope of FG Sge. During maxima of the J brightness, the mean spectral energy distribution at 0.36–5 µm can be represented as a combination of radiation from a G0 supergiant that is attenuated by a dust envelope with a mean optical depth of 0.65±0.15 and emission from the spherically symmetrical dust envelope itself, with the temperature of the graphite grains being 750±150 K. At minima of the J brightness, only radiation from the dust envelope is observed at 1.65–5 µm, with the radiation from the supergiant barely detectable at 1.25 µm. As a result, the integrated flux during J minima is almost half that during J maxima. The mean mass of the spherically symmetrical dust envelope of FG Sge in 1992–2001 was (3 ± 1) × 10−7 M ⊙. This envelope’s mass varied by nearly a factor of two during 1992–2001, in the range (2 – 4) × 10−7 M ⊙. In Autumn 1992, the mass-loss rate from the supergiant exceeded 2 × 10−7 M ⊙/yr. The average rate at which matter was injected into the envelope during 1993–2001 was 10−8 M ⊙/yr. The mean rate of dissipation of the dust envelope was about 1 × 10−8 M ⊙/yr. During 1992–2001, the supergiant lost about 8.7 × 10−7 M ⊙. The parameters of the dust envelope were relatively constant from 1999 until the middle of 2001.

The brightness and color variations of the symbiotic star CH Cygni are studied, and its stationary, spherically symmetric, extended dust envelope is modeled based on long-term UBVRJHKLM photometry, the mid-IR spectral energy distribution (7–23 µm), and far-IR fluxes measured by IRAS and ISO. The existence of a hot dust envelope, detected earlier in the near IR, is confirmed; the optical depth of the envelope has probably increased with time. Model fits to the IRAS and ISO data indicate that the V-band optical depth increased from 0.22 to 0.41 due to dust density enhancement during the 14 years between the observations by the two spacecraft. The mass-loss rate, gas-expansion velocity at the outer boundary of the envelope, and upper limit of the mass of the central source of emission are estimated assuming that the stellar wind of the system is driven by the pressure of the red giant's radiation on the dust, with subsequent momentum transfer to the gaseous medium.

Brightness and color variations of V1016 Cyg are studied using many years of UBVRJHKLM photometric observations and information about its spectral energy distribution in the intermediate IR (7.7 to 22.7 µm) obtained with the IRAS and ISO low-resolution spectrometers. Models for its stationary, spherically symmetrical, extended dust envelope are computed for two cases of heating: by the radiation of the cool component only and by the combined radiation from both components. Model fitting of the IRAS and ISO observations shows that the model with a single central source—the Mira star—provides a better fit to the data, indicating that the hot component’s radiation is appreciably reprocessed by the ambient gas medium and has almost no direct influence on the IR spectrum of the symbiotic nova. The mean spectral energy distributions measured by IRAS in 1983 and ISO on October 1, 1996, differ considerably. The observed evolution of the envelope’s spectrum probably reflects an increasing grain concentration and decreasing grain temperature at the inner edge of the envelope, associated with decreased luminosity and increased temperature of the hot component. The total mass-loss rate, gas-expansion velocity at the outer edge of the envelope, and upper limit to the mass of the central radiation source are estimated.

We have studied the brightness and color variations of the symbiotic nova HM Sge based on longterm UBVRJHKLM photometry of the star and data on its energy distribution in the middle infrared (7.7–22.7 µm) obtained with the low-resolution spectrometers of the IRAS satellite and ISO orbital observatory. We have also calculated models for the steady-state, spherically symmetrical, extended dust envelope of the star for two extreme heating cases: heating only by radiation from the cool component of the system and by the combined radiation from both components. Model fitting to the IRAS and ISO data indicates that models with a single, central Mira-type source are more appropriate. This indicates that the radiation of the hot component is largely processed by the surrounding gas, and does not substantially affect the infrared spectrum of the symbiotic nova directly. The mean spectral energy distribution based on 1983 IRAS data differs appreciably from the ISO spectrum obtained on October 1, 1996. The observed evolution of the envelope spectrum probably reflects an increase of the density and decrease of the temperature of the dust grains near the inner boundary of the envelope, related to a decrease of the luminosity and increase of the temperature of the hot component. We estimate the total mass-loss rate, velocity of gas expansion at the outer envelope boundary, and upper limit for the mass of the central source of radiation.

We present the results of long-term (1978–1998) infrared and optical observations of the unique symbiotic system CH Cygni. The system’s IR brightness and color variations are generally consistent with a model in which the source is surrounded by a dust envelope with variable optical depth. There was evidence for a hot source in the CH Cyg system during the entire period from 1978 to 1998, with the exception of several hundred days in 1987–1989. Over the observation period, there was tendency for the system to gradually redden at 0.36–5 µm, accompanied by a brightness decrease at 0.36–2.2µm and a brightness increase at 3.5 and 5 µm. The “activation” of the cool sources in 1986–1989 nearly coincided with the disappearance of radiation from the hot source. The dust envelope of CH Cyg is not spherically symmetrical, and its optical depth along the line of sight is substantially lower than its emission coefficient, the mean values being τex(L)∼0.06 and τem(L)∼0.16. We confirm the presence of a 1800-to 2000-day period in both the optical and IR, both accounting for, and not accounting for, a linear trend. The spectral type of the cool star varied between M5III and M7III. The spectral type was M5III during the phase of maximum activity of the system’s hot source, while the spectral type was M7III when the star’s optical radiation was almost completely absent. The luminosity of the cool giant varied from (6300–9100)L⊙; its radius varied by approximately 30%. The ratio of the luminosities of the dust envelope and the cool giant varied from 0.08 to 0.5; i.e., up to 50% of the cool star’s radiation could be absorbed in the envelope. The temperature of dust particles in the emitting envelope varied from 550 to 750 K; the radius of the envelope varied by more than a factor of 2. The expansion of the emitting dust envelope observed in 1979–1988 accelerated: its initial velocity (in 1979) was ∼8 km/s, while the maximum velocity (in 1987–1989) was ∼180 km/s. Beginning in 1988, the radiation radius of the dust envelope began to decrease, first at ∼45 km/s and then (in 1996–1998) at ∼3 km/s. From 1979 until 1996, the mass of the emitting dust envelope increased by approximately a factor of 27 (the masses in 1979 and 1988 were ∼1.4×10−7M⊙ and ∼3.8×10−6M⊙, respectively), after which (by 1999) it decreased by nearly a factor of 7. The mass-loss rate of the cool star increased in 1979–1989, reaching ∼3.5×10−6 ∼3.5×10−6M⊙/yr in 1988. Subsequently (up to the summer of 1999), the envelope itself began to lose mass at a rate exceeding that of the cool star. The largest input of matter to the envelope occurred after the phase of optical activity in 1978–1985. If the envelope’s gas-to-dust ratio is ∼100, the mass of matter ejected in 1988 was ∼4×10−4M⊙.