A Model of the Mira–Type Star T UMi

Stellar evolution calculations were carried out from the main sequence to the final stage of the asymptotic giant branch for stars with initial masses 1 M_⊙ ≤ M_ZAMS ≤ 2 M_⊙ and metallicity Z = 0.01. Selected models of evolutionary sequences were used as initial conditions for solution of the equations of radiation hydrodynamics and time–dependent convection describing radial stellar pulsations. The study was aimed to construct the hydrodynamic models of Mira–type stars that show the secular decrease in the pulsation period Π commenced in 1970th at Π = 315 day. We show that such a condition for the period change is satisfied with evolutionary sequences 1 M_⊙ ≤ M_ZAMS ≤ 1.2 M_⊙ and the best agreement with observations is obtained for M_ZAMS = 1.2 M_⊙. The pulsation period reduction is due to both the stellar radius decrease during the thermal pulse of the helium burning shell and mode switch from the fundamental mode to the first overtone. Theoretical estimates of the fundament parameters of the star at the onset of pulsation period reduction are as follows: the mass is M = 0.93 M_⊙, the luminosity is L = 4080 L_⊙, and the radius is R = 220 R_⊙. The mode switch occurs 35 years after the onset of period reduction.     

Radial pulsations of helium stars with masses from 10 to 50<Emphasis Type="Italic">M</Emphasis><Subscript>⊙</Subscript>

We have performed hydrodynamic calculations of the radial pulsations of helium stars with masses 10M_⊙ ≤ M ≤ 50M_⊙, luminosity-to-mass ratios 5 × 10³L_⊙/M_⊙ ≤ L/M ≤ 2.5 × 10⁴L_⊙/M_⊙, and effective temperatures 2 × 10⁴ K ≤ T_eff ≤ 10⁵ K for helium and heavy-element mass fractions of Y=0.98 and Z=0.02, respectively. We show that the high-temperature boundary of the instability region for radial pulsations at L/M ? 10⁴L_⊙/M_⊙ extends to T_eff≈10⁵ K. The amplitude of the velocity variations for outer layers is several hundred km s^?1, while the brightness variations in the B band of the UBV photometric system are within the range from several hundredths to half a magnitude. At constant luminosity-to-mass ratio, the radial pulsation period is determined only by the effective temperature of the star. In the ranges of luminosity-to-mass ratios 10⁴L_⊙/M_⊙ ≤ L/M ≤ 2 × 10⁴L_⊙/M_⊙ and effective temperatures 5 × 10⁴ K ≤ T_eff ≤ 9 × 10⁴ K, the periods of the radial modes are within 6 min ?Π?10³ min.     

Theoretical rates of pulsation period change in the Galactic Cepheids

Theoretical estimates of the rates of radial pulsation period change in Galactic Cepheids with initial masses 5.5 M _⊙ ≤ M _ZAMS ≤ 13 M _⊙, chemical composition X = 0.7, Z = 0.02 and periods 1.5 day ≤ Π ≤ 100 day are obtained from consistent stellar evolution and nonlinear stellar pulsation computations. Pulsational instability was investigated for three crossings of the instability strip by the evolutionary track in the HR diagram. The first crossing occurs at the post-main sequence helium core gravitational contraction stage which proceeds in the Kelvin-Helmholtz timescale whereas the second and the third crossings take place at the evolutionary stage of thermonuclear core helium burning. During each crossing of the instability strip the period of radial pulsations is a quadratic function of the stellar evolution time. Theoretical rates of the pulsation period change agree with observations but the scatter of observational estimates of \(\dot \Pi\) noticeably exceeds the width of the band \(\left( {\delta \log \left| {\dot \Pi } \right| \leqslant 0.6} \right)\) confining evolutionary tracks in the period-period change rate diagram. One of the causes of the large scatter with very high values of \(\dot \Pi\) in Cepheids with increasing periods might be the stars that cross the instability strip for the first time. Their fraction ranges from 2% for M _ZAMS = 5.5 M _⊙ to 9% for M _ZAMS = 13 M _⊙ and variables α UMi and IX Cas seem to belong to such objects.     

Radial pulsations of helium stars with masses from 1 to 10 <Emphasis Type="Italic">M</Emphasis><Subscript>⊙</Subscript>

We present the results of our hydrodynamic calculations of radial pulsations in helium stars with masses 1 M_⊙ ≤ M ≤ 10 M_⊙, luminosity-to-mass ratios 1 × 10³L_⊙/M_⊙ ≤ L/M ≤ 2 × 10⁴L_⊙/M_⊙, and effective temperatures 2 × 10⁴ K ≤ T_eff ≤ 10⁵ K for mass fractions of helium Y=0.98 and heavy elements Z=0.02. We show that the lower boundary of the pulsation-instability region corresponds to L/M ～ 10³L_⊙/M_⊙ and that the instability region for L/M ? 5 × 10³L_⊙/M_⊙ is bounded by effective temperatures T_eff ? 3 × 10⁴ K. As the luminosity rises, the instability boundary moves into the left part of the Hertzsprung-Russell diagram and radial pulsations can arise in stars with effective temperatures T_eff ? 10⁵ K at L/M ? 7 × 10³L_⊙/M_⊙. The velocity amplitude for the outer boundary of the hydrodynamic model increases with L/M and lies within the range 200 ? ΔU ? 700 km s^?1 for the models under consideration. The periodic shock waves that accompany radial pulsations cause a significant change of the gas-density distribution in the stellar atmosphere, which is described by a dynamic scale height comparable to the stellar radius. The dynamic instability boundary that corresponds to the separation of the outer stellar atmospheric layers at a superparabolic velocity is roughly determined by a luminosity-to-mass ratio L/M ～ 3 × 10⁴L_⊙/M_⊙.     

Graphite grain formation in the atmospheres of R coronae borealis stars

The results of calculations of graphite grain formation in the atmospheres of R CrB stars are given. The parameters for the models wereM=1M _⊙,M _bol=?6 mag. The effective temperature ranged from 5300K to 8300K. The chemical composition corresponded to the hydrogen-deficient carbon rich mixture:X=0,Y=0.9,Z _c=0.1. The results obtained show the existence of a critical mass loss rate which is ranged fromM _*≈10^?6 M _⊙yr^?1 forT _eff=5300 K toM _*≈10^?5 M _⊙ yr^?1 forT _eff=8300 K. As soon as the rate of mass loss exceedsM _* by 3–5 times the degree of condensation of carbon changes from 0 to 0.7. The finite radii of grains are about from 0.01 μm to 0.6 μm depending on the density near the condensation point, the velocity of matter outflow, and the stellar effective temperature. The duration of grain growth should amount to some dozens of days. It is supposed that the most probable explanation of dust-shell formation around R CrB stars is graphite condensation behind a shock wave arising from nonlinear stellar pulsation.     

Continuum spectrum of the star Θ1 Ori C

Published photoelectric measurements over a wide wavelength range (0.36–18 µm) are used to study the continuum spectrum of the star Θ¹ Ori C. The model that assumes the following three radiation sources is consistent with observations: (1) a zero-age main-sequence O7 star (object 1) of mass M ₁=20M _⊙, radius R ₁=7.4R _⊙, effective temperature T ₂=37 000 K, and absolute bolometric magnitude $M\mathop {bol}\limits^1 = - 7\mathop .\limits^m 7$ ; (2) object 2 with M ₂=15M _⊙, R ₂=16.2R _⊙, T ₂=4000 K, and $M\mathop {bol}\limits^2 = - 5\mathop .\limits^m 1$ ; and (3) object 3 with R ₃10 700 R _⊙, T ₃=190 K, and $M\mathop {bol}\limits^3 = - 0\mathop .\limits^m 6$ . The visual absorption toward the system is $A_V = 0\mathop .\limits^m 95$ and obeys a normal law. The nature of objects 2 and 3 has not been elucidated. It can only be assumed that object 2 is a companion of the primary star, its spectral type is K7, and it is in the stage of gravitational contraction. Object 3 can be a cocoon star and a member of the system, but can also be a dust envelope surrounding the system as a whole.     

Study of physical properties of spectroscopic binary stars

The main results of a study of a catalogue of physical parameters of 1041 spectroscopic binaries are presented. The distribution of spectroscopic binaries over all main parametersM ₁, a, e, M₁/M₂, P, and certain dependencies between some of them have been found.

1. It appears that among bright (m _v?3 ^m –5 ^m ) stars withM?1M _⊙, about 40% are apparently spectroscopic binaries with comparable masses of components.
2. The majority of spectroscopic binaries with the ratio of the large semiaxis of the orbit to the radius of the primarya/R ₁?20, have eccentricities close to zero. This is probably a consequence of the tidal circularization of orbits of close binaries by viscous friction.
3. The discovery of duplicity of double-line spectroscopic binaries is possible only if the semiamplitude of radial velocityK ₁ is almost 10 times higher than the semiamplitude of the radial velocity of a single-line spectroscopic binary of the same mass.
4. Double-line spectroscopic binaries witha/R _⊙?6(M ₁/M _⊙)^1/3,M ₁≈M ₂?1.5M _⊙ are almost almost absent, and the number of stars witha/R _⊙?6(M ₁/M _⊙)^1/3,M ₁≈1.5M _⊙ is relatively low.
5. The distribution of unevolved SB stars over the large semiaxis may be described by the expression d(N _d/N_t)≈0.2 d loga for 6(M ₁/M _⊙)^1/3?a/R _⊙?100.
6. The intial mass-function for primaries of spectroscopic binaries is the same Salpeter function dN _d≈M ₁ ^?2.35 dM ₁ for 1?M ₁/M _⊙?30.
7. It is possible to explain the observed ratio of the number of single-line spectroscopic binaries to the number of double-line binaries if one assumes that the average initial mass ratio is close to 1 and that the mass of the postmass-exchange remnant of the primary exceeds the theoretical one and/or that half of the angular momentum of the system is lost during mass-exchange.
8. The above-mentioned distributions ofM ₁ anda and assumptions on the mass of remnant and/or momentum loss also allow us to explain the observed shapes of dN/dM, dN/dq, and dN/da distributions after some selection effects are taken into account.

     

Close binary system GO Cyg

In this study, we present long term photometric variations of the close binary system GO Cyg. Modelling of the system shows that the primary is filling Roche lobe and the secondary of the system is almost filling its Roche lobe. The physical parameters of the system are M₁ = 3.0 ± 0.2M_⊙, M₂ = 1.3 ± 0.1M_⊙, R₁ = 2.50 ± 0.12R_⊙, R₂ = 1.75 ± 0.09R_⊙, L₁ = 64 ± 9L_⊙, L₂ = 4.9 ± 0.7L_⊙, and a = 5.5 ± 0.3R_⊙. Our results show that GO Cyg is the most massive system near contact binary (NCB). Analysis of times of the minima shows a sinusoidal variation with a period of 92.3 ± 0.5 yr due to a third body whose mass is less than 2.3M_⊙. Finally a period variation rate of −1.4 × 10⁻⁹ d/yr has been determined using all available light curves.     

Nonlinear pulsations of red supergiants

Excitation of radial oscillations in population I (X = 0.7, Z = 0.02) red supergiants is investigated using the solution of the equations of radiation hydrodynamics and turbulent convection. The core helium burning stars with masses 8M _⊙ ≤ M ≤ 20M _⊙ and effective temperatures T _eff < 4000 K are shown to be unstable against radial pulsations in the fundamental mode. The oscillation periods range between 45 and 1180 days. The pulsational instability is due to the κ-mechanism in the hydrogen and heliumionization zones. Radial pulsations of stars with mass M < 15M _⊙ are strictly periodic with the light amplitude ΔM _bol ≤ 0?5. The pulsation amplitude increases with increasing stellar mass and for M > 15M _⊙ the maximum expansion velocity of outer layers is as high as one third of the escape velocity. The mean radii of outer Lagrangean mass zones increase due to nonlinear oscillations by ≤30% in comparison with the initial equilibrium. The approximate method (with uncertainty of a factor of 1.5) to evaluate the mass of the pulsating red supergiant with the known period of radial oscillations is proposed. The approximation of the pulsation constant Q as a function of the mass-to-radius ratio is given. Masses of seven galactic red supergiants are evaluated using the period-mean density relation.     

Nonlinear RR Lyrae models with new livermore opacities

A. N. Cox recently showed that a 20% opacity decrease in the 20,000-30,000 K region as indicated by the new Livermore OPAL opacities reconciles the discrepancy between pulsation and evolution masses of double-mode RR Lyrae variables. Nonlinear hydrodynamic calculations were performed for RR Lyrae models of mass 0.75M , 51L , andZ = 0.0001 (Osterhoff II type) including this opacity decrease. The Stellingwerf periodic relaxation method was used to converge the models to a limit cycle, and the Floquet matrix eigenvalues calculated to search for a tendency of the fundamental mode to grow from the full-amplitude overtone solution, and the overtone mode to grow from the full-amplitude fundamental solution, thereby predicting double-mode behavior. Models ofT _eff < 7000 K with the opacity decrease have positive fundamental-mode growth rates in the overtone solution, in contrast to earlier results by Hodson and Cox (1982), and models withT _eff > 7000 have positive 1st overtone growth rates in the fundamental-mode solution, but double-mode behavior was not found.     

Speckle interferometric binary system HD375; Is it a sub-giant binary?

Atmospheric modeling is used to build synthetic spectral energy distributions (SEDs) for the individual components of the speckle interferometric binary system HD375. These synthetic SEDs are combined together for the entire system and compared with its observed SED in an iterative procedure to achieve the best fit. Kurucz blanketed models and the measurements of magnitude differences were used to build these SEDs. The input physical parameters for building these best fitted synthetic SEDs represent adequately enough properties of the system. These parameters are: T _eff ^a = 6100 ± 50 K, T _eff ^b = 5940 ± 50 K, log g _a = 4.01 ± 0.10, log g _b = 3.98 ± 0.10, R _a = 1.93 ± 0.20R _⊙, R _b = 1.83 ± 0.20R _⊙, M _v ^a = 3 _· ^m 26 ± 0.40, M _v ^b = 3 _· ^m 51 ± 0.50, L _a = 4.63 ± 0.80 L _⊙, and L _b = 3.74 ± 0.70 L _⊙, in accordance with the new estimated parallax π = 12.02 ± 0.60 mas. A modified orbit of the system is built and compared with earlier orbits, and the masses of the two components are calculated as M _a = 1.35M _⊙ and M _b = 1.25M _⊙. Based on the estimated physical and geometrical parameters of the system, which are confirmed by synthetic photometry, we suggest that the two components are evolved subgiant (F8.5 IV and G0 IV) stars with the age of 3.5 Gyr, formed by fragmentation.     

Neglected reverse Algol system: WZ Hor

This paper presents the first analysis of spectroscopic and photometric observations of the eclipsing binary star WZ Hor. Observations of the system were made at the Mt. John University Observatory in 2007. Since the light contribution of the secondary component was merely 2-3% of the total light of the system in the optical wavelengths, the radial velocity of the primary component could only be determined using the cross-correlation method. A single-lined spectroscopic orbital solution of WZ Hor was obtained, and the BVRI light curves of the system and radial velocity curve of the primary component were analysed simultaneously using the Wilson-Devinney method. The results describe WZ Hor as a reverse Algol-like binary star with a detached configuration. The following absolute parameters of the components were also derived: M₁ = 1.51 ± 0.03 M_⊙, M₂ = 0.66 ± 0.01 M_⊙, R₁ = 1.62 ± 0.02 R_⊙, R₂ = 0.66 ± 0.01 R_⊙, L₁ = 4.93 ± 0.64 L_⊙ and L₂ = 0.09 ± 0.02 L_⊙. The distance to WZ Hor was calculated as 95 ± 8 pc using distance modulus with correction for interstellar extinction, in agreement with the HIPPARCOS value.     

Early-type W UMa contact binary system: New data on V535 Ara

This paper presents the results of spectroscopic and photometric observations of the early-type W UMa system V535 Ara. New high-resolution spectra were taken at the Mt. John University Observatory in 2007. Radial velocities and spectroscopic orbital elements of the system were determined by applying KOREL spectral disentangling. The resulting orbital elements were: a₁sini = 0.0047 ± 0.0001 AU, a₂sini = 0.0146 ± 0.0001 AU, M₁sin³i = 1.85 ± 0.01 M_⊙, and M₂sin³i = 0.59 ± 0.01 M_⊙. The components were found to be in synchronous rotation following examination of their disentangled Hγ line profiles. Four photometric data-sets (1966 BV, 1967 BV, HIPPARCOS and ASAS) were modeled using the Wilson-Devinney method. The model describes V535 Ara as an A sub-type W UMa type eclipsing binary which has a fill out factor of 0.22 in marginal contact configuration. The simultaneous solution of light and radial velocity curves gave the following absolute parameters: M₁ = 1.94 ± 0.04 M_⊙, M₂ = 0.59 ± 0.02 M_⊙, R₁ = 2.09 ± 0.03 R_⊙, R₂ = 1.23 ± 0.02R_⊙, L₁ = 18 ± 3 L_⊙ and L₂ = 6 ± 1 L_⊙. The distance to V535 Ara was calculated as 123 ± 20 pc using distance modulus with correction for interstellar extinction.     

Spectroscopic studies of southern-hemisphere Cepheids: Three Cepheids in Crux (BG Cru,R Cru,and T Cru)

This paper is devoted to spectroscopic studies of three bright Cepheids (BG Cru, R Cru, and T Cru) and continues the series of our works aimed at determining the atmospheric parameters and chemical composition of southern-hemisphere Cepheids. We have studied 12 high-resolution spectra taken with the 1.9-m telescope of the South African Astronomical Observatory and the 8-m VLT telescope of the European Southern Observatory in Chile. The atmospheric parameters and chemical composition have been determined for these stars. The averaged atmospheric parameters are: T _eff = 6253 ± 30 K, log g = 2.15, V _t = 4.30 km s^?1 for BG Cru; T _eff = 5812 ± 22 K, log g = 1.65, V _t = 3.80 km s^?1 for R Cru; and T _eff = 5588 ± 21 K, log g = 1.70, V _t = 4.30 km s^?1 for T Cru. All these Cepheids exhibit a nearly solar metallicity ([Fe/H] = +0.04 dex for BG Cru, +0.06 dex for R Cru, and +0.08 dex for T Cru); the carbon, oxygen, sodium, magnesium, and aluminum abundances suggest that the objects have already passed the first dredge-up. The abundances of other elements are nearly solar. An anomalous behavior of the absorption lines of metals (neutral atoms and ions) in the atmosphere of the small-amplitude Cepheid BG Cru is pointed out. The main components in these lines split up into additional blue and red analogs that are smaller in depth and equivalent width and vary with pulsation phase. Such splitting of the absorption lines of metals (with the hydrogen lines being invariable) is known for the classical Cepheid X Sgr. The calculated nonlinear pulsation model of BG Cru with the parameters L = 2000 L _⊙, T _eff = 6180 K, and M = 4.3M _⊙ shows that this small-amplitude Cepheid pulsates in the first overtone and is close to the blue boundary of the Cepheid instability strip. According to the model, the extent of the Cepheid’s atmosphere is relatively small. Therefore, no spectroscopic manifestations of shock waves through variability are possible in this Cepheid and the observed blue and red components in metal absorption lines can be explained solely by the presence of an extended circumstellar envelope around BG Cru.     

First photometric study of the W UMa system GSC 1042-2191

We present new photometric observations covering eight minima times for the eclipsing binary GSC 1042-2191. The light curves in $\mathit{BVRI}$ colors were analyzed by using WD-code for the system parameters. Eight minima times were obtained from the new observations. The system is found a low mass ratio (q = 0.148), A-type over-contact binary with a fill out parameter of f = 65.01 ± 12.18%. The preliminary absolute dimensions (M₁= 1.26 ± 0.06 M_⊙, M₂ = 0.18 ± 0.06 M_⊙, R₁ = 1.54 ± 0.20 R_⊙, R₂ = 0.69 ± 0.01 R_⊙, ${\mathit{L}}_1$ =3.30 ± 0.30 L_⊙ and ${\mathit{L}}_2$ = 0.59 ± 0.20 L_⊙) indicate the very much oversized and over-luminous secondary component, by assuming the present luminosity of the secondary is its main sequence luminosity, we predict the original mass is about 0.8 M_⊙, this means the present secondary could be transferred and/or lost 77% of its original mass and only its core is left.     

Analysis of EUV limb-brightening observations from ATM

Limb-brightening curves for EUV resonance lines of O vi and Mg x have been constructed from spectroheliograms (5″ resolution) of quiet limb regions observed with the Harvard experiment on Skylab. The observations are interpreted with a simple model for the transition layer and the corona. A comparison of theoretical and observed limb-brightening curves indicates that the lower boundary of the corona, where T _e= 10⁶K, is at a height of about 8000 km in typical quiet areas. For 1.01 R _⊙?r1.25 R _⊙, the corona can be represented by a homogeneous model in hydrostatic equilibrium with a temperature of 10₆K for 1.01 R _⊙?r<1.1 R _⊙ and 1.1 × 10₆K for r?1.1 R _⊙. The model for the transition layer is inhomogeneous, with the temperature gradient a factor of 3 shallower in the network than in the intranetwork regions. It appears that spicules should be included in the model in order to account for the penetration into the corona of cool (T _e<10⁶K) EUV-emitting material to heights up to 20000 km above the limb.     

Spectrographic study of the eclipsing binary system SZ Camelopardalis

Thirteen high-dispersion spectrographs of the eclipsing binary star SZ Cam have been studied with a view of determining more accurate information on: (i) the spectral type and luminosity classifications, (ii) absolute parameters for the component stars, (iii) the stellar environment of SZ Cam. The main results in these categories are as follows: (i) O9.5 Vnk, (ii)m _g=19±2M _⊙,m _s=6.5±1M _⊙;r _g=9.7±3.6R _⊙,r _s=4.8±1.7R _⊙;T _e～30000 K,T _e～23000 K; (iii) there is a local concentration of absorbing material which may reach a density of 2M _⊙ pc^?3, and the distance of the star is found to be 600±150 pc. The determined overluminosity of the secondary star and the local concentration of absorbing material are two topics which provide the basis for a discussion section.     

New spectrophotometry for SZ cam (the problem of a third component)

We present the results of our spectroscopic observations of the eclipsing binary SZ Cam performed with the 1-m (Zeiss-1000) and 6-m (BTA) telescopes at the Special Astrophysical Observatory of the Russian Academy of Sciences in 2000 and 2003. Based on our results and published data, we have calculated new values for the component mass ratio, q = 0.72 ± 0.02, the radial velocity of SZ Cam relative to the Solar system barycenter, V ₀ =?10.6 ± 2.0 km s^?1, and the semi-amplitudes of the radial velocity curves for both components, K ₁ = 192.0 ± 2.6 and K ₂ = 266.4 ± 2.5 km s^?1. The orbital semimajor axes and masses of the components have been determined: α₁ = 10.4R _⊙, α₂ = 14.5R _⊙, M ₁ = 16.7M _⊙, M ₂ = 12.0M _⊙. New light elements and parameters of the radial velocity curve for the third body have been obtained. The mass of the secondary component of the third body M ₂ ^3b is discussed. Its lower limit is estimated to be M ₂ ^3b = 1.4M _⊙.     

Infrared photometry of the symbiotic novae V1016 Cyg and HM Sge in 1978–1999

The photometric JHKLM observations of the symbiotic novae V1016 Cyg and HM Sge in 1978–1999 are presented. Parameters of the cool stars themselves and the dust envelopes are estimated. The periods of 470±5 days (for V1016 Cyg) and 535±5 days (for HM Sge) are reliably determined from the entire set of our photometric J data for V1016 Cyg and HM Sge. In addition, monotonic light and color variations are observed on a time scale of several thousand days, with the increase in infrared brightness occurring with the simultaneous decrease in infrared color indices; i.e., the dust envelopes in which both components of the systems were embedded before the outburst of their hot sources in 1964 and 1975, respectively, had continued to disperse until late 1999. The amplitudes of these variations for HM Sge are almost twice those for V1016 Cyg. For HM Sge, the dust envelope reached a maximum density near JD 2447500 and then began to disperse. In the case of V1016 Cyg, a maximum density of the dust envelope was probably reached near JD 2444800, and its dispersal has been continuing for about 20 years. Thus, in both symbiotic novae, their dust envelopes reached a maximum density approximately eight years after the outburst of the hot component and then began to disperse. An analysis of the color-magnitude (J–K, J) diagram reveals that grains in the dust envelopes of V1016 Cyg and HM Sge are similar in their optical properties to impure silicates. The observed [J–K, K–L] color variations for the symbiotic novae under study can be explained in terms of the simple model we chose by variations in the Mira's photospheric temperature from 2400 to 3000 K and in the dust-envelope optical depth from 1 to 3 at a wavelength of 1.25 µm for a constant grain temperature. The observed J–K and K–L color indices for both symbiotic novae, while decreasing, tend to the values typical of Miras. The dust envelopes of both symbiotic novae are optically thick. The dust envelope around HM Sge is, on the average, twice as dense as that around V1016 Cyg; the Mira in V1016 Cyg is slightly cooler (~2800–2900 K) than that in HM Sge (~2600–2700 K). The dust-envelope density decreases as the Mira's temperature increases. The absolute bolometric magnitudes are $ - 5\mathop .\limits^m 1 \pm 0\mathop .\limits^m 15$ for V 1016 Cyg and $5\mathop .\limits^m 27 \pm 0\mathop .\limits^m 17$ for HM Sge. Their distances are 2.8±0.6 and 1.8±0.4 kpc, respectively; the luminosities and radii of their cool components (Miras) are 8.6×10³ L _⊙, 1×10⁴ L _⊙, 500R _⊙, and 540R _⊙. The radii of their dust envelopes are 1400R _⊙ and 1500R _⊙; the masses are (3?3.3) × 10^?5M_⊙ and (4?8) × 10^?5M_⊙ The dust envelope of V1016 Cyg disperses slower than that of HM Sge by almost a factor of 25.