On time variations of the intensity of galactic cosmic rays for the recent billion years from the data on exposure ages of iron meteorites

To ascertain probable variations of the intensity of galactic cosmic rays (GCR) for the recent billion years, the distribution of exposure ages T of iron meteorites has been analyzed. We considered all ~80 values of ages from the data by Voshage and Feldmann (1979), Voshage et al. (1983), and Voshage (1984), as well as a set of values obtained from the correction for eliminating the meteorites formed in a single collision. To correct the data, the Akaike information criterion was used. For the distributions of the phase values Ph = T/t–int(T/t), the dependence of the criterion χ ² on the presumable period t in the exposure age variations was analyzed. For t ~ 400–500 Myr and, partly, for t ~ 150 Myr, the significant deviations of this criterion from the corresponding mean values were found. To clear up the influence of the GCR intensity variations on the age distribution, the numerical models were calculated with an account of the set of ages randomly distributed in the interval of 0–1000 Myr with the presumptive mean lifetime of iron meteorites in outer space τ = 700 Myr. It has been ascertained that, for variations with a period of t = 450 Myr, the distribution of exposure ages of the model set is similar to that found for iron meteorites. The obtained data suggest that the GCR intensity variations with a period of approximately 400–500 Myr have probably existed during the recent billion years. These variations may be caused by periodic passages of the Solar System through spiral arms of the Galaxy. It has been shown that the earlier discussed changes in the GCR intensity with a period of ~150 Myr (Shaviv, 2002; 2003; Scherer et al., 2006) are less defined.     

GJ 900: A new hierarchical system with low-mass components

Speckle interferometric observations made with the 6 m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences in 2000 revealed the triple nature of the nearby (π _Hip = 51.80 ± 1.74 mas) low-mass young (≈ 200 Myr) star GJ 900. The configuration of the triple system allowed it to be dynamically unstable. Differential photometry performed from 2000 through 2004 yielded I- and K-band absolute magnitudes and spectral types for the components to be I _A =6.66±0.08, I _B =9.15±0.11, I _C =10.08±0.26, K _A =4.84±0.08, K _B =6.76±0.20, K _C =7.39±0.31, Sp _A ≈K5?K7, Sp _B ≈M3?M4, Sp _C ≈M5?M6. The “mass-luminosity” relation is used to estimate the individual masses of the components: M _A ≈0.64M _⊙, M _B ≈0.21M _⊙, M _C ≈0.13M _⊙. From the observations of the components’ relative motion in the period 2000–2006, we conclude that GJ 900 is a hierarchical triple star with the possible orbital periods P_A-BC≈80 yrs and P_BC≈20 yrs. An analysis of the 2MASS images of the region around GJ 900 leads us to suggest that the system can include other very-low-mass components.     

Catalog of red clump candidates in Tycho-2

We present the technique we used to compile a catalog of about 61 000 local stars brighter than K _s = 8.2 ^m which were identified as most likely red clump candidates on the basis of their reduced proper motions in the K _s band. The catalog was compiled from the combined Tycho-2 and 2MASS data for the stars with color indices J-K _s ranging from 0.5 ^m to 0.8 ^m . It includes the equatorial coordinates, the proper motions, the magnitudes B _T , V _T , J, H, and K _s , and the probabilities for the stars to be red clump giants.     

Evolutionary studies of the young star clusters: NGC 1960, NGC 2453 and NGC 2384

We report the analysis of the young star clusters NGC 1960, NGC 2453 and NGC 2384 observed in the J (1.12 μm), H (1.65 μm) and K′ (2.2 μm) bands. Estimates of reddening, distance and age as E(B?V)=0.25, d=1380 pc and t=31.6 to 125 Myr for NGC 1960, E(B?V)=0.47, d=3311 pc and t=40 to 200 Myr for NGC 2453 and E(B?V)=0.25, d=3162 pc and t=55 to 125 Myr for NGC 2384 have been obtained. Also, we have extended the color–magnitude diagrams of these clusters to the fainter end and thus extended the luminosity functions to fainter magnitudes. The evolution of the main sequence and luminosity functions of these clusters have been compared with themselves as well as Lyngå 2 and NGC 1582.     

Irregular dwarf galaxy KK 230: A relatively young galaxy at the periphery of the local group?

We present some results of the photometric analysis of the stellar population of the irregular dwarf galaxy KK 230 on the basis of the archive database of the Hubble space telescope. The color index-magnitude diagram for KK 230 gets to magnitude 27 ^m in the V and I bands, and it comprises stellar populations of various ages. The age of the youngest main-sequence stars is 3.2 × 10⁷ yr. These stars are distributed along the north-south direction in the picture plane, and this fact can be linked to the observed kinematics of the neutral gas in the galaxy. Older blue and red supergiants are no less than 1.6 × 10⁸ years old, and such an age implies that the star formation was episodic over the last several hundreds of millions of years. As judged from the position of the tip of the red giant branch, the distance modulus for KK 230 is m ? M = 26.5 ^m . The corresponding distance is D = 2 Mpc. Based on the average absolute magnitude M _I,RC and color index (V ? I)_I,RC of the red clump, we conclude that the majority of KK 230 stars have an age of no more than (2–3) × 10⁹ yr, their metallicity being Z ≈ 0.0004.     

Einstein–Maxwell Field Equation in Isotropic Coordinates: An Application to Modeling Superdense Star

We present a charged analogue of Pant et al. (2010, Astrophys. Space Sci., 330, 353) solution of the general relativistic field equations in isotropic coordinates by using simple form of electric intensity E that involve charge parameter K. Our solution is well behaved in all respects for all values of X lying in the range 0 <X≤ 0.11, K lying in the range 4 <K≤ 6.2 and Schwarzschild compactness parameter u lying in the range 0 <u≤ 0.247. Since our solution is well behaved for wide ranges of the parameters, we can model many different types of ultra-cold compact stars like quark stars and neutron stars. We have shown that corresponding to X = 0.077 and K = 6.13 for which u = 0.2051 and by assuming surface density ρ _b =4.6888×10¹⁴ g cm ^?3 the mass and radius are found to be 1.509M _⊙, 10.906 km respectively which match with the observed values of mass 1.51M _⊙ and radius 10.90 km of the quark star XTE J1739-217. The well behaved class of relativistic stellar models obtained in this work might have astrophysical significance in the study of more realistic internal structures of compact stars.     

The evolutionary status of the semiregular variable QY Sge

Repeated spectroscopic observations made with the 6-m telescope of SAO RAS yielded new data on the radial-velocity variability of the anomalous yellow supergiant QY Sge. The strongest and most peculiar feature in its spectrum is the complex profile of NaI D lines, which contains a narrow and a very wide emission components. The wide emission component can be seen to extend from ?170 to +120 km/s, and at its central part it is cut by an absorption feature, which, in turn, is split into two subcomponents by a narrow (16 km/s at r=2.5) emission peak. An analysis of all the Vr values leads us to adopt for the star a systemic velocity of V_r=?21.1 km/s, which corresponds to the position of the narrow emission component of NaI. The locations of emission-line features of NaI D lines are invariable, which point to their formation in regions that are external to the supergiant’s photosphere. Differential line shifts of about 10 km/s are revealed. Emission in the Hα line is weaker than in NaI D lines, it fills the photospheric absorption almost completely. The absorption lines in the spectrum of QY Sge have a substantial width of FWHM ≈ 45 km/s. The method of model atmospheres is used to determine the following parameters: the effective temperature T _eff =6250±150 K, surface gravity l _{g g}=2.0±0.2, and microturbulence velocity ξ _t =4.5±0.5 km/s. The chemical composition of the atmosphere differs only slightly from the solar composition: the metallicity of the star is found to be somewhat higher than the solar metallicity with an average overabundance of iron-peak elements of [Met/H]_⊙=+0.20. The star is found to be slightly overabundant in carbon and nitrogen, [C/Fe]=+0.25, [N/Fe]=+0.27. The α-process elements Mg, Si, and Ca are slightly overabundant, on the average by [α/H]_⊙=+0.12, and sulfur overabundance is higher, [S/α]=+0.29. The strong overabundance of sodium, [Na/Fe]=+0.75, is likely to be due to the dredge-up of the matter processed in the NeNa cycle. Heavy elements of the s-process are underabundant relative to the Sun. On the whole, the observed properties of QY Sge do not give grounds for including this star into the group of RCrB or RVTau-type objects.     

Evolution of Intergalactic Gas in the Neighborhood of Dwarf Galaxies and Its Manifestations in the HI 21 cm Line

Low-mass galaxies are known to have played the crucial role in the hydrogen reionization in the Universe. In this paper we investigate the contribution of soft x-ray radiation (E ~ 0.1–1 keV) from dwarf galaxies to hydrogen ionization during the initial reionization stages. The only possible sources of this radiation in the process of star formation in dwarf galaxies during the epochs preceding the hydrogen reionization epoch are hot intermediate-mass stars (M ~ 5–8 M_⊙) that entered the asymptotic giant branch (AGB) stage and massive x-ray binaries. We analyze the evolution of the intergalactic gas in the neighborhood of a dwarf galaxy with a total mass of 6 × 10⁸M_⊙ formed at the redshift of z ~ 15 and having constant star-formation rate of 0.01–0.1 M_⊙ yr^?1 over a starburst with a duration of up to 100 Myr. We show that the radiation from AGB stars heats intergalactic gas to above 100 K and ensures its ionization x_e ? 0.03 within about 4–10 kpc from the galaxy in the case of a star-formation rate of star formation 0.03–0.1 M_⊙ yr^?1, and that after the end of the starburst this region remains quasi-stationary over the following 200–300 Myr, i.e., until z ~ 7.5. Formation of x-ray binaries form in dwarf galaxies at z ~ 15 results in a 2–3 and 5–6 times greater size of the ionized and heated region compared to the case where ionization is produced by AGB stars exclusively, if computed with the “x-ray luminosity–star-formation rate” dependence (L_X ~ f_XSFR) factor f_X = 0.1 and f_X ~ 1, respectively. For f_X ? 0.03 the effect of x-ray binaries is smaller that that of AGB star population. Lyα emission, heating, and ionization of the intergalactic gas in the neighborhood of dwarf galaxies result in the excitation of the 21 cm HI line. We found that during the period of the starburst end at z ~11.5–12.5 the brightness temperature in the neighborhood of galaxies is 15–25 mK and the region where the brightness temperature remains close to its maximum has a size of about 12–30 kpc. Hence the epoch of the starburst end is most favorable for 21 cm HI line observations of dwarf galaxies, because at that time the size of the region of maximum brightness temperature is the greatest over the entire evolution of the dwarf galaxy. In the case of the sizes corresponding to almost 0.’1 for z ~ 12 regions with maximum emission can be detected with the Square Kilometre Array, which is currently under construction.     

Moments of inertia and the Chandlerian period for two-and three-layer models of the Galilean satellite Io

We consider two-layer (Fe-FeS core+silicate mantle) and three-layer (Fe-FeS core+silicate mantle+crust) models of the Galilean satellite Io. Two parameters are known from observations for the equilibrium figure of the satellite, the mean density ρ₀ and the Love number k₂. Previously, the Radau-Darwin formula was used to determine the mean moment of inertia. Using formulas of the Figure Theory, we calculated the principal moments of inertia A, B, and C and the mean moment of inertia I for the two-and three-layer models of Io using ρ₀ and k₂ as the boundary conditions. We concluded that when modeling the internal structure of Io, it is better to use the observed value of k₂ than the moment of inertia I derived from k₂ using the Radau-Darwin formula. For the models under consideration, we calculated the Chandlerian wobble periods of Io. For the three-layer model, this period is approximately 460 days.     

Fundamental parameters and intrinsic colors of F,G, and K supergiants and classical cepheids

We used high-resolution echelle spectra with high signal-to-noise ratio to determine with a high degree of accuracy some atmospheric parameters (T _eff, log g and [Fe/H]) for 68 non-variable supergiants of types F, G, and K and 26 classical Cepheids in 302 pulsation phases. Very accurate effective temperatures, with errors of only 10–30 K, were determined by the line-depth ratio method. We found that the observed intrinsic color indices (B ? V)₀ can be related to these parameters: (B ? V)₀ = 57.984? 10.3587(log T _eff)² + 1.67572(log T _eff)³ ? 3.356 log g+ 0.321 V _t + 0.2615[Fe/H] + 0.8833log g(log T _eff). With this empirical relation, the intrinsic colors of individual supergiants and classical Cepheids of spectral types F0-K0 and of luminosity classes I and II can be estimated with an accuracy as high as 0.05 ^m , which is comparable to the accuracy of the most elaborate photometric procedures. In view of large distances to supergiants, the method we propose here allows a large-scale mapping of interstellar extinction with an accuracy of 0.1–0.2 ^m in a quite large region of the Galaxy.     

A photometric study of faint galaxies in the field of GRB 000926

We present our B, V, R_c, and I_c observations of a \(3'.6 \times 3'\) field centered on the host galaxy of GRB 000926 (α_2000.0=17^h04^m11^s, \(\delta _{2000.0} = + 51^ \circ 47'9\mathop .\limits^{''} 8\)). The observations were carried out on the 6-m Special Astrophysical Observatory telescope using the SCORPIO instrument. The catalog of galaxies detected in this field includes 264 objects for which the signal-to-noise ratio is larger than 5 in each photometric band. The following limiting magnitudes in the catalog correspond to this limitation: 26.6 (B), 25.7 (V), 25.8 (R), and 24.5 (I). The differential galaxy counts are in good agreement with previously published CCD observations of deep fields. We estimated the photometric redshifts for all of the cataloged objects and studied the color variations of the galaxies with z. For luminous spiral galaxies with M(B)z～1.     

OB stars in the Tycho-2 and 2MASS catalogues

The Tycho-2 proper motions and five-band Tycho-2 and 2MASS photometry for approximately 2.5 million common stars have been used to select OB stars and to determine the extinction and photometric distance for each of them. We have selected 37 485 stars and calculated their reddenings based on their positions in the two-color V _T -H, J-Ks diagrams relative to the zero-age main sequence and the theoretical reddening line for B5 stars. Tests confirm that the selected stars belong to the spectral types O-B with a small admixture of later types. We calculate the extinction coefficient R and its variations with Galactic longitude based on the positions of the selected stars in the two-color B _T -V _T , V _T -Ks diagram. The interstellar extinction for each star is calculated as the product of the reddening found and the coefficient R. The extinction and its variations with Galactic longitude agree well with the extinction based on the model by Arenou et al. (1992). Calibration of the relation between the absolute magnitude and reduced proper motion V _T − + 5 + 5 log μ for Hipparcos stars has allowed us to calculate the absolute magnitudes and photometric distances for the selected stars. The distances found agree with those derived from the Hipparcos parallaxes within 500 pc. The distribution of the stars and the extinction variations with distance found show that the selected stars form an almost complete sample of stars with spectral types earlier than B5 within about 750 pc of the Sun. The sample includes many noticeably reddened stars in the first and second Galactic quadrants that are absent from the Hipparcos and Tycho Spectral Types Catalogues. This slightly changes the pattern of the distribution of OB stars compared to the classical pattern based on Hipparcos. Original Russian Text ? G.A. Goncharov, 2008, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2008, Vol. 34, No. 1, pp. 10–20.     

Open clusters IC 4665 and Cr 359 and a probable birthplace of the pulsar PSR B1929+10

Based on the epicyclic approximation, we have simulated the motion of the young open star clusters IC 4665 and Collinder 359. The separation between the cluster centers is shown to have been minimal 7 Myr ago, 36 pc. We have established a close evolutionary connection between IC 4665 and the Scorpius-Centaurus association — the separation between the centers of these structures was ≈200 pc 15 Myr ago. In addition, the center of IC 4665 at this time was near two well-known regions of coronal gas: the Local Bubble and the North Polar Spur. The star HIP 86768 is shown to be one of the candidates for a binary (in the past) with the pulsar PSR B1929+10. At the model radial velocity of the pulsar V _r = 2 ± 50 km s^?1, a close encounter of this pair occurs in the vicinity of IC 4665 at a time of ?1.1 Myr. At the same time, using currently available data for the pulsar B1929+10 at its model radial velocity V _r = 200 ± 50 km s^?1, we show that the hypothesis of Hoogerwerf et al. (2001) about the breakup of the ζ Oph-B1929+10 binary in the vicinity of Upper Scorpius (US) about 0.9 Myr ago is more plausible.     

Infrared luminosities of local-volume galaxies

Based on data from the Two-Micrometer All-Sky Survey (2MASS), we analyzed the infrared properties of 451 Local-Volume galaxies at distances D ≤ 10 Mpc. We determined the K-band luminosity function of the galaxies in the range of absolute magnitudes from ?25^m to ?11^m. The local luminosity density within 8 Mpc is 6.8 × 10⁸L_⊙ Mpc^?3, a factor of 1.5 ± 0.1 higher than the global mean K-band luminosity density. We determined the ratios of the virial mass to the K-band luminosity for nearby groups and clusters of galaxies. In the luminosity range from 5 × 10¹⁰ to 2 × 10¹³L_⊙, the dependence log(M/L_K) ∝ (0.27 ± 0.03) log L_K with a dispersion of ～0.1 comparable to the measurement errors of the masses and luminosities of the systems of galaxies holds for the groups and clusters of galaxies. The ensemble-averaged ratio, 〈M/L_K〉 ? (20–25) M_⊙/L_⊙, was found to be much smaller than the expected global ratio, (80–90)M_⊙/L_⊙, in the standard model with Ω_m = 0.27. This discrepancy can be eliminated if the bulk of the dark matter in the Universe is not associated with galaxies and their systems.     

Spectroscopic studies of yellow supergiants in the Cepheid instability strip

High-resolution spectra of nine yellow nonvariable supergiants (NVSs) located within the canonical Cepheid instability strip from Sandage and Tammann (1969) (α Aqr, ? Leo, μ Per, ω Gem, BD+60 2532, HD 172365, HD 187299, HD 190113, and HD 200102) were taken with the 1-m Zeiss and 6-m BTA telescopes at the Special Astrophysical Observatory of the Russian Academy of Sciences in the 1990s. These have been used to determine the atmospheric parameters, chemical composition, radial velocities, reddenings, luminosities, distances, and radii. The spectroscopic estimates of T _eff and the luminosities determined from the Hipparcos parallaxes have shown eight of the nine program NVSs on the T _eff?log(L/L _⊙) diagram to be outside the canonical Cepheid instability strip. When the edges of the Cepheid instability strip from Bono et al. (2000) are used, out of the NVSs from the list on the diagram one is within the Cepheid instability strip but closer to the red edge, two are at the red edge, three are beyond the red edge, two are at the blue edge, and one is beyond the blue edge. The evolutionary masses of the objects have been estimated. The abundances of α-elements, r- and s-process elements for all program objects have turned out to be nearly solar. The СNO, Na, Mg, and Al abundance estimates have shown that eight of the nine NVSs from the list have already passed the first dredge-up. Judging by the abundances of the key elements and its position on the T _eff?log(L/L _⊙) diagram, the lithium-rich supergiant HD 172365 is at the post-main-sequence evolutionary stage of gravitational helium core contraction and moves toward the first crossing of the Cepheid instability strip. The star ? Leo should be assigned to bright supergiants, while HD 187299 and HD 190113 may have already passed the second dredge-up and move to the asymptotic branch.     

Photometric observations of Cepheids from the ASAS-3 catalog: Photoelectric <Emphasis Type="Italic">BV I</Emphasis><Subscript>c</Subscript> observations of 46 low-amplitude Cepheids

From December 2006 to January 2008, we performed 1699 BV I _c observations for 46 low-amplitude Cepheids discovered in the course of the ASAS project using the 76-cm telescope of the South-African Astronomical Observatory (SAAO). We provide the tables of observations and V light and B-V and V-I _c color curves. These new observations, along with data from the ASAS-3 catalog, have been used to improve the elements of the light variations. Our data allow the number of known Galactic low-amplitude Cepheids to be almost doubled. This makes it possible to increase the number of distance indicators suitable for studying the structure of the inner Galactic arms by almost 15%.     

Evolutionary status and chemical composition of the atmosphere of the spectroscopic and speckle interferometric binary HD 10009

HD 10009 is a spectroscopic and speckle interferometric binary with almost identical solar-type components. It was studied via speckle interferometry using the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences and had its spectrophotometry performed in the 3500–9600 Å wavelength interval with the 2-m telescope of the Terskol Branch of the Institute of Astronomy of the Russian Academy of Sciences. A detailed analysis of the atmosphere of the primary component (component 1) of the binary yielded the abundances of some of the elements. The luminosities and temperatures of the components are found to be L ₁= 2.9 L _⊙, L ₂= 1.0 L _⊙ and T _eff1=6017 K, T _eff2=5930 K, respectively. The iron abundance is [Fe]=?0.27±0.05. Our results make it possible to assess the evolutionary status of the system. The binary is 7.9 Gyr old and the primary component is close to become a red giant, whereas the secondary component is still in the hydrogen-burning stage near the main sequence.     

Preheating of the early universe by radiation from high-mass X-ray binaries

Using a reliablymeasured intrinsic (i.e., corrected for absorption effects) present-day luminosity function of high-mass X-ray binaries (HMXBs) in the 0.25–2 keV energy band per unit star formation rate, we estimate the preheating of the early Universe by soft X-rays from such systems. We find that X-ray irradiation, mainly executed by ultraluminous and supersoft ultraluminous X-ray sources with luminosity L _X > 10³⁹ erg s^?1, could significantly heat (T >T _CMB, where T _CMB is the temperature of the cosmic microwave background) the intergalactic medium by z ~ 10 if the specific X-ray emissivity of the young stellar population in the early Universe was an order of magnitude higher than at the present epoch (which is possible due to the low metallicity of the first galaxies) and the soft X-ray emission from HMXBs did not suffer strong absorption within their galaxies. This makes it possible to observe the 21 cm line of neutral hydrogen in emission from redshifts z < 10.     

A Comprehensive Study of 94 Open Clusters Based on the Data from IPHAS,GAIA DR2, and Other Sky Surveys

We determine the color excesses, photometric distances, ages, astrometric parallaxes and proper motions for 94 open clusters in the northern part of the Milky Way. We estimate the color excesses and photometric distances based on the data from IPHAS photometric survey of the northern Galactic plane using individual total-to-selective extinction ratios R_r = A_r/E_r?i for each cluster computed via the color-difference method based on IPHAS r, i, and Hα-band, 2MASS J-, H-, and K_s-band, WISE W1-band, and Pan-STARRS i-, z-, and y-band data. The inferred R_r values vary significantly from cluster to cluster spanning the R_r = 3.1–5.2 interval with a mean and standard deviation equal to 〈R_r〉 = 3.99 and σR_r = 0.34, respectively.We identified cluster members using (1) absolute proper motions determined from individual-epoch positions of stars retrieved from IPHAS, 2MASS,URAT1, ALLWISE,UCAC5, and Gaia DR1 catalogs and positions of stars on individual Palomar Sky Survey plates reconstructed based on the data provided in USNO-B1.0 catalog and (2) absolute proper motions provided in Gaia DR2 catalog, and computed the averageGaia DR2 trigonometric parallaxes and propermotions of the clusters. Themean formal error of the inferred astrometric parallaxes of clusters is of about 7 μas, however, a comparison of astrometric and photometric parallaxes of our cluster sample implies that Gaia DR2 parallaxes are, on the average, systematically underestimated by 45 ± 9 μas. This result agrees with estimates obtained by other authors using other objects. At the same time, we find our photometric distance scale to be correct within the quoted errors (the inferred correction factor is equal to unity to within a standard error of 0.025).     

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.